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Moreland Hills, Ohio

Moreland Hills is a village in eastern Cuyahoga County, Ohio, United States. The population was 3,466 at the 2020 census. An eastern suburb of Cleveland, it is part of the Cleveland metropolitan area.

History
In 1815, settlement began near the point where State Route 87 crosses the Chagrin River. Orange Township was established in 1820 and became known for its steam sawmills, cheese factories and farms. The village, which in 1831 was still part of Orange Township, was the birthplace of James A. Garfield, the 20th President of the United States. In 1897, the Cleveland-Chagrin Falls Railway spurred residential development in the area as it served as a commuter line to employment opportunities in Cleveland.

In the early 20th century, Orange Township was divided into five municipalities, Moreland Hills, Hunting Valley, Orange Village, Pepper Pike and Woodmere. Moreland Hills was incorporated as a village in 1929, encompassing the southeast quadrant of the original Orange Township. Moreland Hills adopted a village charter in 1972, defining the municipal corporation with a mayor-council form of government.

What is known as the Orange Conference in the history of the Church of Jesus Christ of Latter-day Saints (LDS) took place from October 25–26, 1831, in what is now Moreland Hills. It occurred at the home of Serenes Burnett, located at the southeast corner of today's Ohio Route 87 and Chagrin River Road (not the house that now occupies the site). The three leading figures in the church at that time, Joseph Smith, Sidney Rigdon, and Oliver Cowdery were in attendance.

Moreland Hills is home to state historical landmark Hiram House, the country's second settlement house after Hull House in Chicago. Hiram House moved its operations from Cleveland to its current site at Harvard Road and State Route 91 in the 1940s.

Geography
Moreland Hills is located at 41.44056°N, -81.42528°W (41.440456, -81.425210).

According to the United States Census Bureau, the village has a total area of 7.23 sqmi, of which 7.15 sqmi is land and 0.08 sqmi is water.

2010 census
As of the census of 2010, there were 3,320 people, 1,262 households, and 1,009 families living in the village. The population density was 464.3 PD/sqmi. There were 1,376 housing units at an average density of 192.4 /sqmi. The racial makeup of the village was 89.6% White, 3.7% African American, 0.1% Native American, 4.6% Asian, 0.1% Pacific Islander, 0.3% from other races, and 1.7% from two or more races. Hispanic or Latino of any race were 1.1% of the population.

There were 1,262 households, of which 32.7% had children under the age of 18 living with them, 71.6% were married couples living together, 5.6% had a female householder with no husband present, 2.8% had a male householder with no wife present, and 20.0% were non-families. 17.4% of all households were made up of individuals, and 8.2% had someone living alone who was 65 years of age or older. The average household size was 2.63 and the average family size was 2.97.

The median age in the village was 49.1 years. 24.2% of residents were under the age of 18; 4.2% were between the ages of 18 and 24; 14.4% were from 25 to 44; 38.8% were from 45 to 64; and 18.6% were 65 years of age or older. The gender makeup of the village was 49.3% male and 50.7% female.

2000 census
As of the census of 2000, there were 3,298 people, 1,286 households, and 1,014 families living in the village. The population density was 455.0 PD/sqmi. There were 1,341 housing units at an average density of 185.0 /sqmi. The racial makeup of the village was 93.00% White, 3.03% African American, 0.03% Native American, 3.24% Asian, 0.09% from other races, and 0.61% from two or more races. Hispanic or Latino of any race were 0.67% of the population.

There were 1,286 households, out of which 31.8% had children under the age of 18 living with them, 72.5% were married couples living together, 4.9% had a female householder with no husband present, and 21.1% were non-families. 19.1% of all households were made up of individuals, and 9.7% had someone living alone who was 65 years of age or older. The average household size was 2.56 and the average family size was 2.93.

In the village, the population was spread out, with 23.1% under the age of 18, 4.3% from 18 to 24, 18.3% from 25 to 44, 36.5% from 45 to 64, and 17.7% who were 65 years of age or older. The median age was 48 years. For every 100 females, there were 94.2 males. For every 100 females age 18 and over, there were 91.3 males.

The median income for a household in the village was $113,977, and the median income for a family was $134,621. Males had a median income of $100,000 versus $42,054 for females. The per capita income for the village was $72,001. About 1.3% of families and 3.3% of the population were below the poverty line, including 3.7% of those under age 18 and 3.4% of those age 65 or over.

Education
Moreland Hills is primarily served by the Orange City School System. Small parts of the village are served by the Chagrin Falls Exempted Village School District.

Notable people

 * James A. Garfield, 20th President of the United States (then named Orange Township)
 * Ellis Burks, former Major League Baseball player and former special assistant to the general manager of the then Cleveland Indians
 * Vanessa Bayer, actress and comedian, cast member on Saturday Night Live (2010-2017)
 * Robert E. Murray, CEO of Murray Energy Corporation
 * Diana Munz, Olympic swimmer
 * Ben Wallace, forward in the NBA

title: Moreland Hills, Ohio


text:
Newburgh Heights, Ohio

Newburgh Heights is a village in Cuyahoga County, Ohio, United States. The population was 1,862 at the 2020 census. A suburb of Cleveland, it is a part of the Cleveland metropolitan area.

Geography
Newburgh Heights is surrounded on three sides (west, north and east) by Washington Park Blvd, north of Harvard Avenue, and west of the Willow Freeway (I-77) at 41.45°N, -81.66667°W (41.450, -81.660).

According to the United States Census Bureau, the village has a total area of 0.58 sqmi, all land.

Demographics
As of the 2000 census, the center of population in Cuyahoga County was located in Newburgh Heights, near East 26th Street.

96.0% spoke English, 3.4% Polish, and 0.7% Spanish.

2010 census
As of the census of 2010, there were 2,167 people, 958 households, and 536 families residing in the village. The population density was 3736.2 PD/sqmi. There were 1,145 housing units at an average density of 1974.1 /sqmi. The racial makeup of the village was 79.1% White, 14.9% African American, 0.1% Native American, 0.3% Asian, 2.3% from other races, and 3.2% from two or more races. Hispanic or Latino of any race were 5.4% of the population.

There were 958 households, of which 30.7% had children under the age of 18 living with them, 28.7% were married couples living together, 19.1% had a female householder with no husband present, 8.1% had a male householder with no wife present, and 44.1% were non-families. 37.4% of all households were made up of individuals, and 10.7% had someone living alone who was 65 years of age or older. The average household size was 2.26 and the average family size was 2.96.

The median age in the village was 37.2 years. 24.8% of residents were under the age of 18; 8.7% were between the ages of 18 and 24; 25.5% were from 25 to 44; 28.4% were from 45 to 64; and 12.6% were 65 years of age or older. The gender makeup of the village was 51.0% male and 49.0% female.

2000 census
As of the census of 2000, there were 2,389 people, 1,052 households, and 621 families residing in the village. The population density was 4,104.3 PD/sqmi. There were 1,157 housing units at an average density of 1,987.7 /sqmi. The racial makeup of the village was 94.47% White, 3.14% African American, 0.21% Native American, 0.13% Asian, 0.54% from other races, and 1.51% from two or more races. Hispanic or Latino of any race were 2.47% of the population.

There were 1,052 households, out of which 25.4% had children under the age of 18 living with them, 36.8% were married couples living together, 17.4% had a female householder with no husband present, and 40.9% were non-families. 33.9% of all households were made up of individuals, and 11.8% had someone living alone who was 65 years of age or older. The average household size was 2.27 and the average family size was 2.91.

In the village, the population was spread out, with 21.6% under the age of 18, 8.9% from 18 to 24, 33.6% from 25 to 44, 22.4% from 45 to 64, and 13.5% who were 65 years of age or older. The median age was 37 years. For every 100 females there were 93.0 males. For every 100 females age 18 and over, there were 91.4 males.

The median income for a household in the village was $37,409, and the median income for a family was $42,131. Males had a median income of $37,650 versus $24,969 for females. The per capita income for the village was $18,636. About 9.2% of families and 12.0% of the population were below the poverty line, including 16.9% of those under age 18 and 5.3% of those age 65 or over.

Political controversy
Former mayor Trevor Elkins was accused of illegally using campaign funds for personal reasons from 2015 to 2019. Elkins spent $134,705 over the course of 651 occasions for personal expenditures when those funds cannot be used for such purposes, even if reimbursed by Elkins. He also paid a political consulting firm he owns $8,400 from campaign funds. The Franklin County Prosecutor's Office is expected to take up the case and has said that a felony charge is "fully on the table." The Ohio Elections Commission has voted to refer the case for prosecution by a vote of 5-2. Elkins also has admitted to misusing more than $134,100 of his campaign funds on 650 occasions from 2015 to 2019, using a campaign debit card to cover routine personal expenses. He said he always repaid the account and did not realize what he was doing was illegal until it was pointed out to him.

Former Newburgh Heights mayor Trevor Elkins, accused of elections-related offenses, agreed to plead guilty to three misdemeanor charges. According to the Franklin County Prosecutor's Office, Elkins agreed that he will plead guilty to one count of attempted theft in office and two counts of attempted election falsification. He also agreed to step down from his position as mayor once he entered those guilty pleas. Prosecutors accused Elkins of dipping into his campaign account 650 times between 2015 and 2019, totaling more than $134,000. Elkins told the Ohio Elections Commission last month that he put his own money into the campaign account and sometimes withdrew it for personal use. "It's like a bank robbery," special prosecutor Brian Simms told FOX 8. "You commit a bank robbery, and you return to the bank and give them back their money. Well, guess what? You still committed a bank robbery." The prosecutor's office also says Elkins agreed to shut down his campaign account and can not run for any Cuyahoga County elected office for the 2024-2028 term.

Traffic enforcement
Newburgh Heights is a nationally-known speed trap, employing traffic cameras along a very short stretch of Interstate 77 that runs through it. In addition, traffic cameras are employed in the stretch of Harvard Avenue that leads to the I-77 on ramp. The penalties range from $150.00 to $300.00.

Former mayor Trevor Elkins said in 2017 his village issues about 300 speeding tickets per week from using its one hand-held camera. He said the system is safer than when officers pull over speeding drivers, and he disagreed with critics who might say the camera is a cash grab. "The people who are speeding are not victims," Elkins said. "They were breaking the law, and they got caught." 25% of the city revenue comes from traffic tickets. The national average is at least ten times lower, at approximately 2%.

Mayor Elkins has stated publicly that he defends the use of the cameras and admits they generate revenue, and said in 2016, "do I recognize that they generate revenue? Absolutely. Do I apologize for that? No."

As of July 3, 2019, Ohio Governor Mike DeWine signed into law legislation that reduces state funding for any city, town, or village operating red light or speed cameras by an amount equivalent to the fines collected. (The provision withholding state funding has been enjoined by the 8th District Court of Appeals) The law requires all appeals of tickets received through camera technology to be heard in court rather than by an administrative officer.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Newburgh Heights, Ohio


text:
North Randall, Ohio

North Randall is a village in Cuyahoga County, Ohio, United States. The population was 954 at the 2020 census. A suburb of Cleveland, it is a part of the Cleveland metropolitan area.

History
Settlement at North Randall began in earnest in the 1850s when the Cleveland & Mahoning Railroad was extended to that point. North Randall was incorporated as a village in 1908.

Geography
North Randall is located at 41.43111°N, -81.53056°W (44.431203, -81.530582).

According to the United States Census Bureau, the village has a total area of 0.77 sqmi, all land.

Demographics
97.45% spoke English and 2.55% Tagalog.

2010 census
As of the census of 2010, there were 1,027 people, 462 households, and 209 families living in the village. The population density was 1333.8 PD/sqmi. There were 571 housing units at an average density of 741.6 /sqmi. The racial makeup of the village was 10.2% White, 86.3% African American, 0.9% Native American, 1.3% Asian, 0.2% from other races, and 1.2% from two or more races. Hispanic or Latino of any race were 0.7% of the population.

There were 462 households, of which 21.4% had children under the age of 18 living with them, 19.0% were married couples living together, 20.8% had a female householder with no husband present, 5.4% had a male householder with no wife present, and 54.8% were non-families. 51.1% of all households were made up of individuals, and 14.5% had someone living alone who was 65 years of age or older. The average household size was 1.84 and the average family size was 2.69.

The median age in the village was 51.2 years. 15.2% of residents were under the age of 18; 6.8% were between the ages of 18 and 24; 19.8% were from 25 to 44; 31% were from 45 to 64; and 27.4% were 65 years of age or older. The gender makeup of the village was 42.8% male and 57.2% female.

2000 census
As of the census of 2000, there were 906 people, 465 households, and 211 families living in the village. The population density was 1,158.8 PD/sqmi. There were 490 housing units at an average density of 626.7 /sqmi. The racial makeup of the village was 21.08% White, 71.74% Black or African American, 0.33% Native American, 0.99% Asian, 2.98% from other races, and 2.87% from two or more races. Hispanic or Latino of any race were 7.28% of the population.

There were 465 households, out of which 20.4% had children under the age of 18 living with them, 22.6% were married couples living together, 18.7% had a female householder with no husband present, and 54.6% were non-families. 51.0% of all households were made up of individuals, and 13.8% had someone living alone who was 65 years of age or older. The average household size was 1.80 and the average family size was 2.62.

In the village, the population was spread out, with 16.3% under the age of 18, 10.4% from 18 to 24, 32.1% from 25 to 44, 24.7% from 45 to 64, and 16.4% who were 65 years of age or older. The median age was 40 years. For every 100 females there were 94.8 males. For every 100 females age 18 and over, there were 94.9 males.

The median income for a household in the village was $28,235, and the median income for a family was $38,580. Males had a median income of $31,154 versus $25,417 for females. The per capita income for the village was $20,938. About 5.6% of families and 11.4% of the population were below the poverty line, including 9.3% of those under age 18 and 7.3% of those age 65 or over.

Economy
Randall Park Mall opened in 1976 and closed in 2009. Amazon built a new distribution center on the site in 2018.

Education
The Village of North Randall is served by the Warrensville Heights City School District, which has six campuses and an enrollment of approximately 2,500 students.

title: North Randall, Ohio


text:
Talk:Waring's problem

(No title)
Removed this:
 * Using the Hardy-Littlewood method?, g(k) can now readily be computed for all other values of k as well.

Really ? If we had to wait till 1986 to prove g(4)=19, I don't think we can readily compute g(k) yet. And if so, how ? Hardy & Littlewood died long before 1986. FvdP 20:06 Oct 23, 2002 (UTC)

I think this is simply wrong; no such method is known. Thanks for the catch. AxelBoldt 22:27 Oct 23, 2002 (UTC)
 * I guess we have to wait some more time, yes. Axel thank you too for catching the link to wrong Langrange's theorem. --XJamRastafire 00:48 Oct 24, 2002 (UTC)

This seems self-contradictory (emphasis is mine):
 * All other values of g are now also known, as a result of work by Dickson, Pillai, Rubugunday and Niven. Their formula contains two cases, and it is conjectured that the second case never occurs; in the first case, the formula reads g(k) = [...]

So is g known or only conjectured ? If it is known, what is Dickson (etc)'s second case about ? --FvdP 20:03 Feb 17, 2003 (UTC)

The exact value for g(k) is known for every k, in the sense that, if you give me k, I can give you g(k). Dickson's formula has two cases. In order to figure out which case of the formula to use for a particular k, I have to check a certain thing about the number k. If the outcome of that check is "YES", I pick the first case of the formula, if the outcome of the test is "NO", I pick the second case of the formula. Nobody has ever seen a value for k where the outcome was "NO". It is conjectured that there are no such values. Therefore I didn't list the second case of the formula in the article.

Maybe the sentence in the article should be reformulated somehow. AxelBoldt 21:46 Feb 17, 2003 (UTC)

OK, I understand it now. Thanks. My mathematical mind looks a bit rusty. Sad thing. --FvdP

Waring's problem really solved? I think not!
Shouldn't this page be fixed? I really really doubt that g(k) is known for all k now. Dickson's formula only gives conjectured values for g(k). His formula indeed has two cases, one of which is conjectured not to occur, but in any case the outcome of Dickson's formula can be easily computer for arbitrary k. This outcome however is *not* known to be the exact value of g(k). See http://mathworld.wolfram.com/WaringsProblem.html for more information about the condition to be checked in Dickson's formula.

To repeat once more, the statement on this talk page that "The exact value for g(k) is known for every k, in the sense that, if you give me k, I can give you g(k)" is NOT true. What is true is that "if you give me k, I can give you the outcome of Dickson's formula". Dickson's formula gives only a conjectural value for g(k). Dickson's formula is from 1936. The value of g(4) was only proved to be 19 in 1986!

As this page is now, it gives the impression that the real values of g(k) are almost all known by Dickson's formula, and that only an unimportant secondary condition is left to be checked. This is the impression also when you search for Waring's problem on the web, since most information on the problem is now coming from this wikipedia article. So a fix is in order. I could probably do it, but I'd like to hear first what the original authors think of this.

 * The anonymous poster in this section obviously missed the requirement for k to be greater than or equal to 6 in Dickson, et. al.'s formula. In my opinion AxelBoldt's explanation above is correct. Does that mean that the anonymous comment above is "patent nonsense" and should be removed? TheGoblin 16:49, 26 January 2006 (UTC)

 * Hardy and Wright states that indeed g(k) is known for $$k \geq 6$$, but not at all that this was proved by Dickson. They describe it as an ongoing work, with the validity of Dickson's formula proved much later. In other words, Dickson's formula indeed only gave a conjectural value; but the conjecture now is proved.  I think this means that the anonymous protest was a bona fide and not totally unreasonable misunderstanding.-JoergenB (talk) 16:49, 12 January 2008 (UTC)

- - - Vinogradov's bound was improved upon several times according to Ian Stewart (Game, Set and Math). J.R. Chen showed g(n)<= n(3logn+5.2). A more complicated improvement later by Mozzochi and Balasubramanian. Of more interest are the best known individual bounds for G(n) <=g(n), which from Stewart are for n=4,5,6...15: 3,4,7,8,34,32,102,51,135,150,166 and 181.Billymac00 13:49, 31 January 2006 (UTC)

 * Since G(4) is exactly 16 I think Billymac00's list of upper bounds for G(n) seems questionable. He is correct in that Vinogradov's bound has been improved several times... TheGoblin 22:09, 1 March 2006 (UTC)

Formula for g(k)
the formula for g(k) is actually based on a very basic inequality. It is definitely a lower bound always, and the conjecture states that it also is enough. I changed it just before we discuss the formula.Evilbu 15:14, 4 February 2006 (UTC)

Everything is explained clearly here: http://www.mathpages.com/home/kmath316.htm

Who writes this stuff?

 * "Lagrange's four-square theorem was conjectured by Fermat in 1640"

as a special case of his Polygonal Number Theorem? That was 1638. When he proved it I don't know, perhaps two years later is correct, since it wasn't published. Relevant? Barely.

 * "and was first stated in 1621."

Really? Not by Diophantus?

 * "Apart from a certain ambiguity, all the other values of g are now also known, as a result of work by Dickson, Pillai, Rubugunday and Ivan M. Niven."

I have no idea if this is true or not. Mathworld states "Dickson (1936), Pillai (1936), and Niven also conjectured an explicit formula for g(s) for s>6". 59.112.47.213 18:58, 2 September 2006 (UTC)

Big oh
It is somewhat curious to write a formula with big Oh, and claim that it holds for every k. Kope 13:23, 11 July 2007 (UTC)

g(4)
Hardy and Littlewood showed that all sufficiently large numbers are the sum of at most 19 fourth powers contradicts ''g(4) = 19 [was established] in 1986 by R. Balasubramanian, F. Dress, and J.-M. Deshouiller'' because Hardy and Littlewood both died before 1986 and they already knew from trivial computation that 79 requires 19 fourth powers, thus they knew that g(4) = 19. Icek (talk) 17:20, 23 November 2007 (UTC)

 * There is no contradiction. Let's reformulate the two claims. Call S the set of those natural numbers which cannot be written as the sum of 19 fourth powers. Hardy and Littlewood proved that S is finite and B-D-D proved that it is the empty set. This is much stronger and surely not identical. Kope (talk) 13:45, 26 November 2007 (UTC)

 * Sorry - somehow I unintentionally ignored the "sufficiently large" as it seemed unintuitive that smaller numbers would require more fourth powers - I have to be a bit more careful. Icek (talk) 18:39, 26 November 2007 (UTC)

Why analytic?
If Waring's problem is related to analytic number theory, can this link be made clear somehow? What analytic techniques are used in its solution? Thehotelambush (talk) 02:00, 12 November 2008 (UTC) Large quantities of calculus and complex numbers are needed to answer your question. —Preceding unsigned comment added by 81.148.89.37 (talk) 15:11, 8 August 2009 (UTC)

???
Hmm, I am no math wiz or anything, but, the beginning paragraph seems off... does waring's problem really state "19" fourth power numbers? that seems totally random, if it does >.> why wouldn't it be 16?173.28.10.216 (talk) 00:46, 13 January 2010 (UTC)
 * Read down to the first paragraph of the next section. How do you express 79 as a sum of only 16 fourth powers? —David Eppstein (talk) 00:50, 13 January 2010 (UTC)
 * 173.28.10.216 seems to have little or no formal education. —Preceding unsigned comment added by 93.97.194.200 (talk) 16:24, 28 September 2010 (UTC)
 * I sympathize with the first comment, however little formal education the commenter may or may not have had. Waring's conjecture, as given by various sources, was that “Every number is the sum of 4 squares; every number is the sum of 9 cubes; every number is the sum of 19 fourth powers; and so on."  The first two numbers appear to show a pattern:  4 is the square of 2, and 9 is the square of 3, so if the apparent pattern continues we might expect the next number to be 16, the square of 4, but in fact it is given as 19.  It would be reasonable to suspect a typo or printer's error (setting a 6 upside down to give 19 instead of 16).  I accept that 19 is indeed correct, but it breaks the apparent pattern and seems to come out of the blue.  Perhaps there is no pattern after all.  But if so, what did Waring mean by 'and so on'?  This seems to imply not only a continuing pattern, but a continuing pattern which ought to be obvious to the reader.  Not to me, anyway.  Added: see my comment 'What Waring said' below.  This rules out the possibility of a misprint. 2A00:23C8:7907:4B01:94C5:5A34:F356:3D09 (talk) 17:32, 15 June 2022 (UTC)
 * It sometimes helps to actually read a text before commenting on it. The conjectural value 2^k + [1.5^k] - 2 for g(k) is explained in the second paragraph of the article, and does provide a nice pattern. --Sapphorain (talk) 15:32, 19 June 2022 (UTC)

Changes on 14th October
Hi,

I made the changes on 14th October. There were quite a number of obscurities and oversights in the article which I have attempted to correct. For example there was a misleading reference to Euler which should be to his son. The article omitted to mention Vinogradov's important paper of 1959, but mentions Karatsuba's as if it were the breakthrough. p-adic ideas were first introduced in the late 1930s by Davenport as a refinement of the Hardy and Littlewood diminshing ranges technique. In somewhat different ways they were used by Vinogradov and Linnik. J. A. Euler's formula is proved for k <= 471,000,000, and so I added chapter and verse on this. There were quite a number of other things like this. I added a reference to the survey article of Wooley and myself. This is an area where there has been a massive amount of work in since 1920 and the article can only really act as a guide to further reading. If anyone would like to discuss the changes through this talk page please alert me at

rvaughan@math.psu.edu

Bob Vaughan

Rvaughan2000 (talk) 18:57, 16 October 2010 (UTC)

G(4)
Hi, I don't understand the following sentence: "Davenport showed that G(4) = 16 in 1939, by demonstrating that any sufficiently large number congruent to 1 through 14 mod 16 could be written as a sum of 14 fourth powers (Vaughan in 1985 and 1989 reduced the 14 successively to 13 and 12)."

Which of the two 14's mentioned is reduced to 12? If it is the first this doesn't seem to be an improvement. If it is the second this would imply that G(4) = 14, contradicting the statement later in the article that each number of the form 31*16^n requires 16 fourth powers. Ok, now that I am typing this I can think of a third possibility where both 14's are simultatiously lowered to 12. That is probably what is meant but if so the sentence should perhaps be rewritten to make this clearer.

Apart from that: showing that every sufficient large number congruent to 1 through 14 mod 16 can be written as a sum of 14 fourth powers only seems to show that G(4) is at most 16, so maybe the remark about 16 being a lower bound as well (which we find further down the article) should be moved up to this point in the article.

Vincent — Preceding unsigned comment added by Octonion (talk • contribs) 20:24, 5 February 2012 (UTC)

Wooley then established that for some constant C,[20]
[20] The Hardy-Littlewood method, R. C. Vaughan, 2nd ed., Cambridge Tracts in Mathematics, CUP, 1997

I don't see Wooley. Where did he prove his great result? ru:Участник:МетаСкептик12

 * There is a detailed answer in the Zentralblatt review: I have added a link to the citation in the article. Deltahedron (talk) 16:29, 25 July 2012 (UTC)

"Theorized"
The article currently states, "Prior to the posing of Waring's problem, Joseph-Louis Lagrange theorized that any positive integer could be represented as the sum of four perfect squares". "Theorized" is not a word that is used in mathematics: what does it mean? It seems that it must mean either "conjectured" or "proved" but, from the chronology, it's impossible to tell which: Waring posed his problem in 1770 and Lagrange proved the four-square theorem in the same year. I would guess that Waring posed the problem after hearing about Lagrange's proof. On the other hand, it's also possible that Waring posed the general problem and Lagrange heard of this and proved the square case. Does anyone know what actually happened? Dricherby (talk) 10:51, 29 October 2013 (UTC)

John Conway
This article should mention the fact that John Conway found g(5) while he was an undergraduate. 118.210.185.246 (talk) 11:37, 13 March 2014 (UTC)

Copy Editing

 * I removed "there" because it is not grammatically necessary.
 * I changed "... such that ..." with "such ... that ..." because the former is intuitive to people knowing the mathematical "such that" symbol (cursive E) whereas the latter is more intuitive to laypeople, for whom Wikipedia is written.
 * I removed the parenthetical example because its length necessitates a separate clause.

Duxwing (talk) 16:38, 5 April 2014 (UTC)

 * You changed "whether ... there exists X" to "whether ... exists X". This is ungrammatical. "Whether X exists" might be acceptable, but in this case X is such a long phrase that readers would be left for a long time wondering what the verb is. As for whether the second part of the sentence is separated by parens or a semicolon, it seems very unimportant to me; better would have been to make it a separate sentence. —David Eppstein (talk) 16:46, 5 April 2014 (UTC)

 * Why is "there exists" grammatical whereas "exists" alone is not? Perhaps "for every X there is a Y" generally is tortured and should be rewritten "a Y exists for every X".
 * You have not mentioned whether "... such that ..." is better written "such ... that ...": are we therefore agreed that it is?
 * The example is subordinate to the definition and therefore should follow a semicolon.

Duxwing (talk) 02:21, 6 April 2014 (UTC)
 * I'm not exactly sure how to diagram the grammar of "there exists" but it is extremely standard usage in mathematics. "Exists X" is ungrammatical because in English we put the subjects before the verbs.Your use of "such" instead of "such that" seems also strange and unidiomatic to me. Again, "such that" is extremely standard in mathematics. —David Eppstein (talk) 02:31, 6 April 2014 (UTC)

 * *"For Y exists X" is grammatical because English verbs can precede their subjects; e.g., the famous slogan, "Drill, baby, drill!" or the advertising phrase, "For all your X needs, we have Y".
 * *Wikipedian articles and especially their leads are written for the lay, for whom "such ... that ..." is more intuitive than "... such that ..." because the former is standard English whereas the latter uses a term-of-art.

Duxwing (talk) 03:24, 6 April 2014 (UTC)

 * "Drill, baby, drill" is imperative. The rules are different for that mode, and the subject is the implied "You", which is not stated at all so it doesn't come after the verb. "We have Y" has its subject, "We", before its verb. And using standard mathematical phrasing is a better idea than making up your own nonstandard phrasing. In this particular case, it's also important to understand that the phrasing "for every X there exists Y such that every Z has property P" is the prose version of a precise mathematical statement using logical quantification symbols, of the form $$\forall X\exists Y\forall Z P(Z)$$, and that small changes to the text can introduce mathematical errors in that interpretation. —David Eppstein (talk) 04:08, 6 April 2014 (UTC)

 * Pondering this problem last night, I noticed your objection that verbs must follow their subjects also applies to the original lead because "there" is not the sentence's subject: it is a preposition. If it is a preposition, then the preceding prepositional phrase "for..." renders it redundant by already defining the argument's domain.  This redundancy is general, also applying to sentences like "Alexander the Great, he was a brilliant tactician," which should be written "Alexander the Great was a brilliant tactician".  Therefore, you cannot demand that "there" remain by claiming its grammatical necessity.

 * This conclusion also holds in formal notation because "there" also is a pronoun for the domain's antecedent definition, which is included in the sentence and therefore requires no pronoun. The original sentence roughly formally noted therefore would be

 * Where X is true
 * Let Y refer to "X is true"
 * Where Y is true, Z

 * This notation could be transitively reduced to "Where X is true, Z". Also, even if "there" were mathematically necessary, its presence and the following wordy phrase would only confuse our lay readers.

 * Moreover, my notation is not made up; it exists throughout English in sentences like 'in this valley flows a river'. These sentences can become independent clauses in larger sentences like "In this valley flows a river, whose deep blue waters sparkle under the noon sun" or logical statements like "If in this valley flows a river, then cross it with a bridge".  I would only thus write sentences wherein the noun or noun phrase following the verb is long; e.g., "for every natural number K exists such a positive integer S that every natural number is the sum of...".

 * Finally and perhaps fundamentally, the definition is wordy. I cannot parse its language, which, most charitably interpreted, seems to be written by mathematicians for mathematicians.  Duxwing (talk) 18:59, 6 April 2014 (UTC)

 * The phrase complained of appears to conform to standard mathematical English conventions, namely, "for all/each/every X there exists (a/an/) Y such that P(X,Y)". It would be quite unconventional to omit "there".  The example "for every natural number K exists such a positive integer S that every natural number is the sum of..." does not sound like either mathematical or idiomatic English.  Deltahedron (talk) 19:12, 6 April 2014 (UTC)

 * Oh, hello! :) I have long known the "For X exists Y" to be standard, whereas I have not known "there exists" to be standard, often encountering "there is" or "exists" or "is"; would you please show me where I can learn about standard phrasing?  Omitting "there" would be conventional English because "there" is redundant because it literally immediately follows the domain whereto it refers, and writing "such ... that ..." is conventional because "such" describes what follows and "that" describes the effect. Duxwing (talk) 01:35, 7 April 2014 (UTC)

 * Here are a couple of references describing this specific turn of phrase ("there exists").: . More generally for mathematical writing you might also find Knuth's book  helpful. —David Eppstein (talk) 03:33, 7 April 2014 (UTC)

 * Another few:, , . Deltahedron (talk) 06:24, 7 April 2014 (UTC)

 * Wow! Thanks! :) I will consult these daunting texts when confused.  If we want to be accurate without being excessively technical, then an idiomatic defintion in the lead and a symbolic one in the first section would respectively inform the lay and satisfy the learned.  I suggest that this idiomatic definition be my afore-suggested one: "For ... exists such a ... that ...". Duxwing (talk) 01:56, 8 April 2014 (UTC)

 * As we have already said repeatedly, that word ordering is unidiomatic and nonstandard. I suggest we not do that. —David Eppstein (talk) 03:10, 8 April 2014 (UTC)

 * Its being non-standard should not matter in the lead because the lead is not written for laypeople, who would not understand its being non-standard and might be confused by "standard" (no scare-quotes intended) phrasing. Why is my phrasing unidiomatic? The sentence structure I suggest works in other sentences like "in the valley flows a river," wherein the verb precedes the noun, and like "He caused such a ruckus that the neighbors awoke," wherein "such ... that ..." is the structure.  I therefore see no general reason to keep "there" or use the awkward "such that" in the lead, wherein readability must supersede precision lest lay readers should be driven away.  To exemplify unto absurdity, consider non-mathematical sentences written to this technical standard: "in the valley there flows a river" could be a run-on and has an unclear prepositional phrase, and "he caused a ruckus such that the neighbors awoke" is tortured by a linguistic tick.

 * The lead's linguistic ticks transform it from a lay-readable paragraph to a technical journal entry requiring evidently voluminous reading for its first sentence's grammar alone. This transformation and its requirements thus violate sections 2.7.7 and 2.7.8 of Wikipedian policy "What Wikipedia is Not," which state that:

 * 2.7.7 "A Wikipedia article should not be presented on the assumption that the reader is well versed in the topic's field. Introductory language in the lead (and also maybe the initial sections) of the article should be written in plain terms and concepts that can be understood by any literate reader of Wikipedia without any knowledge in the given field before advancing to more detailed explanations of the topic. While wikilinks should be provided for advanced terms and concepts in that field, articles should be written on the assumption that the reader will not or cannot follow these links, instead attempting to infer their meaning from the text."
 * 2.7.8 "Academic language. Texts should be written for everyday readers, not for academics. Article titles should reflect common usage, not academic terminology, whenever possible."

 * Following this policy, I have suggested changing the lead's "academic language," which requires being "well versed in the topic's field" to understand, to the aforementioned "plain terms and concepts," which technical phrases like "there exists" or "... such that ..." evidently are not because I, a layperson, could not understand them. Knowing that accuracy is important, I have suggested also moving this technical description somewhere it will not confuse lay readers; e.g., a sub-heading titled "Formal Definition" including technical English and symbolic notation. Duxwing (talk) 04:25, 8 April 2014 (UTC)

 * This is not the way things work at present. There are numerous ways of expressing the formula $$\forall X exists Y$$ in idiomatic English, such as, "for every X there is a Y" or "there is a Y for each X" or "for all X there exists Y".  Mathematical convention is to use the last of these, which is acceptable English if somewhat stilted.  To omit "there", as in "for all X exists Y" is not idiomatic English.  Arguing by analogy with other constructions is beside the point.  Of the two sentences
 * For every man in this world, there is a woman ready to marry him.
 * For every man in this world, exists a woman ready to marry him.
 * only the first is acceptable English.

 * As for the academic language point, I have explained that the "for all ... there exists" is a choice of idiomatic English. I frankly find it very hard to believe that a native speaker of English cannot understand the sentence "For all X there exists Y" but can readily understand "For all X exists Y".

 * A "literate reader" of an article must be presumed to understand the basic terminology of the subject and it is absurd to suggest that articles would or could be written any other way. It would be ridiculous to suggest that an article on biology could not use terms such as "genus" or "species" or "virus" or "animal" in the introduction, or in physics the word "matter" or "space" or "time" or "energy", or in chemistry the words "molecule" or "atom" or "element" or "compound".  All of these are technical terms in the various subjects.  Do you really expect an article on mice to begin "A mouse is a small furry thing that moves about and eats things that don't move about, belonging to a large group of quite similar moving things which contains some smaller groups of rather more similar small furry moving things."

 * Rewriting the Manual of Style to support your comments here is not the way to resolve this discussion. Deltahedron (talk) 21:25, 10 April 2014 (UTC)

arXiv is not a reliable source
Sorry, but arXiv is not a reliable publication: it contains only preprint-type papers, none of which is peer-reviewed. It is not an acceptable source for an encyclopedia. I am perfectly aware that Trevor Wooley is a more than decent mathematician, who has published a number of good papers in prestigious journals. But, precisely for this reason, if his results are correct they will eventually be published in a regular, peer-reviewed journal: it is only then that wikipedia can convey the (encyclopedic) information concerning them. Wikipedia is not a tabloid. Sapphorain (talk) 15:39, 14 February 2016 (UTC)

What Waring said
The present article does not seem to have a direct citation for Waring's own statement of his 'theorem'. Fortunately, Hilbert's paper of 1909 gives an exact source: Edward Waring, 'Meditationes Algebraicae', 3rd edn., 1782, p. 349-50. This is available at the Internet Archive. The cited pages contain several propositions, of which two (numbers 5 and 9) constitute what is now called Waring's Theorem (or Problem). The Latin text of these propositions is as follows:

5.  Omnis integer numerus est quadratus; vel e duobus, tribus vel quatuor quadratis compositus.

9.  Omnis integer numerus est cubus; vel e duobus, tribus, 4, 5, 6, 7, 8 vel novem cubis compositus:  est etiam quadro-quadratus; vel e duobus, tribus, &c. usque ad novemdecim compositus, & sic deinceps: consimilia etiam affirmari possunt (exceptis excipiendis) de eodem numero quantitatum earundem dimensionum.

I have attempted a literal translation, with some help from Google Translate:

5. Every whole number is a square; or is composed of two, three or four squares.

9. Every whole number is a cube; or is composed of two, three, 4, 5, 6, 7, 8 or nine [novem] cubes:  it is also a fourth power [literally a squared-square]; or is composed of two, three, etc. up to nineteen [novemdecim], and so on [& sic deinceps]: also similar things may be affirmed (with exceptions where exceptions are necessary) about the same number of quantities of the same dimensions. The meaning of the last few words is not clear. I would take it as just a general assertion that similar statements can be made about higher powers. There is nothing to indicate that Waring actually had any formula for higher powers, let alone a proof. I don't know what he means about 'necessary exceptions'.

The Latin text incidentally rules out any possibility that '19' was a printing error for '16', not only because 16 would be incorrect, but because the number 'novemdecim' is printed as a word, not a numeral, and there is hardly a risk of anyone confusing it with the Latin for 'sixteen' ('sedecim').

I have not inserted a citation into the article, but someone else may wish to. I should also note that the text of 1782 is probably not Waring's first statement of his 'theorem', and there may be some variations in earlier editions of his book. I have not looked into this.2A00:23C8:7907:4B01:6448:1E21:4A4C:73C8 (talk) 13:58, 19 June 2022 (UTC)

title: Talk:Waring's problem


text:
North Royalton, Ohio

North Royalton is a city in Cuyahoga County, Ohio, United States. It is a suburb of Cleveland. The population was 31,322 as of the 2020 census. Originally incorporated as a village in 1927, it achieved the status of city in 1961.

History
North Royalton was founded in 1818. Knight Sprague, an early settler, had the township named after his native town in Vermont, Royalton. Sometime between 1880 and 1890, the name of Royalton was changed to North Royalton because of another town in Ohio bearing the same name. On April 4, 1927, the township officially became the Village of North Royalton, and the first mayor, E. C. McCombs, was elected.

Geography
North Royalton is located at 41.32228°N, -81.74639°W.

According to the United States Census Bureau, the city has a total area of 21.32 sqmi, of which 21.31 sqmi is land and 0.01 sqmi is water.

Demographics
As of the census of 2000, there were 28,647 people, 11,250 households, and 7,695 families residing in the city. The population density was 1,345.9 PD/sqmi. There were 11,754 housing units at an average density of 552.2 /sqmi. The racial makeup of the city was 96.18% White, 0.71% African American, 0.12% Native American, 1.99% Asian, 0.02% Pacific Islander, 0.16% from other races, and 0.83% from two or more races. Hispanic or Latino of any race were 0.95% of the population.

There were 11,250 households, out of which 31.5% had children under the age of 18 living with them, 58.4% were married couples living together, 7.4% had a female householder with no husband present, and 31.6% were non-families. 26.7% of all households were made up of individuals, and 7.0% had someone living alone who was 65 years of age or older. The average household size was 2.51 and the average family size was 3.11. The average house cost about $210,000.00.

In the city the population was spread out, with 24.3% under the age of 18, 7.7% from 18 to 24, 30.6% from 25 to 44, 25.4% from 45 to 64, and 12.0% who were 65 years of age or older. The median age was 39 years. For every 100 females, there were 95.2 males. For every 100 females age 18 and over, there were 92.4 males.

The median income for a household in the city was $57,398, and the median income for a family was $69,983. Males had a median income of $46,764.00 versus $31,173.00 for females. The per capita income for the city was $26,610. About 1.2% of families and 2.3% of the population were below the poverty line, including 1.5% of those under age 18 and 3.5% of those age 65 or over.

Of the city's population over the age of 25, 32.9% hold a bachelor's degree or higher.

Languages
96.3% spoke English, 1.5% German, 1.3% Polish, and 0.9% Italian in their house.

2010 census
As of the census of 2010, there were 30,444 people, 12,944 households, and 8,220 families residing in the city. The population density was 1428.6 PD/sqmi. There were 13,710 housing units at an average density of 643.4 /sqmi. The racial makeup of the city was 94.6% White, 1.2% African American, 0.1% Native American, 2.8% Asian, 0.3% from other races, and 1.1% from two or more races. Hispanic or Latino of any race were 1.6% of the population.

There were 12,944 households, of which 26.5% had children under the age of 18 living with them, 52.5% were married couples living together, 7.9% had a female householder with no husband present, 3.1% had a male householder with no wife present, and 36.5% were non-families. 31.0% of all households were made up of individuals, and 10.1% had someone living alone who was 65 years of age or older. The average household size was 2.33 and the average family size was 2.97.

The median age in the city was 43.5 years. 20.1% of residents were under the age of 18; 7.7% were between the ages of 18 and 24; 24.3% were from 25 to 44; 32.7% were from 45 to 64; and 15.1% were 65 years of age or older. The gender makeup of the city was 48.8% male and 51.2% female.

Schools
The North Royalton School District serves approximately 4700 students in the communities of North Royalton and Broadview Hts. Parochial schools
 * North Royalton Elementary School (Grades K–4)
 * North Royalton Middle School (Grades 5–8)
 * North Royalton High School (Grades 9–12)
 * St. Albert the Great School (K-8)
 * Royal Redeemer Lutheran School (K-8)

The High School added a new 60,000 foot math and science wing that will be the replacement for the front 1950 section.

Library
North Royalton's public library is a branch of the Cuyahoga County Public Library (CCPL), the busiest per-capita system in the country. A new building to which all functions have been transferred opened in August 2013, is located two miles north of the city center at 5071 Wallings Road, North Royalton, Ohio. It was formerly located at 14600 State Road (OH-94) with North Royalton's Memorial Park almost adjacent to Route 82. The existing library structure was then converted into a new city hall facility, which opened to the public in 2015.

Notable people

 * Chris Broussard – Former resident, ESPN NBA analyst
 * Erich Gliebe - Former boxer and chairman of National Alliance.

Surrounding communities
North Royalton is bordered by Parma and Middleburg Heights to the north, Broadview Heights to the east, Hinckley to the south, and Strongsville to the west.

title: North Royalton, Ohio


text:
Oakwood, Cuyahoga County, Ohio

Oakwood is a village in Cuyahoga County, Ohio, United States. The population was 3,572 at the 2020 census. An eastern suburb of Cleveland, it is a part of the Cleveland metropolitan area.

Geography
Oakwood is located at 41.36705°N, -81.50378°W. According to the United States Census Bureau, the village has a total area of 3.45 sqmi, of which 3.44 sqmi is land and 0.01 sqmi is water.

2010 census
As of the census of 2010, there were 3,667 people, 1,544 households, and 935 families living in the village. The population density was 1066.0 PD/sqmi. There were 1,648 housing units at an average density of 479.1 /sqmi. The racial makeup of the village was 30.7% White, 64.7% African American, 0.2% Native American, 0.7% Asian, 0.1% Pacific Islander, 0.2% from other races, and 3.4% from two or more races. Hispanic or Latino of any race were 2.3% of the population.

There were 1,544 households, of which 24.6% had children under the age of 18 living with them, 38.3% were married couples living together, 17.2% had a female householder with no husband present, 5.1% had a male householder with no wife present, and 39.4% were non-families. 35.0% of all households were made up of individuals, and 12.3% had someone living alone who was 65 years of age or older. The average household size was 2.28 and the average family size was 2.94.

The median age in the village was 46.7 years. 18.7% of residents were under the age of 18; 7.7% were between the ages of 18 and 24; 21.5% were from 25 to 44; 32.9% were from 45 to 64; and 19.3% were 65 years of age or older. The gender makeup of the village was 47.6% male and 52.4% female.

2000 census
As of the census of 2000, there were 3,667 people, 1,416 households, and 877 families living in the village. The population density was 1,060.1 PD/sqmi. There were 1,480 housing units at an average density of 427.9 /sqmi. The racial makeup of the village was 40.66% White, 56.23% African American, 0.19% Native American, 0.35% Asian, 0.03% Pacific Islander, 0.71% from other races, and 1.83% from two or more races. Hispanic or Latino of any race were 1.39% of the population.

There were 1,416 households, out of which 23.2% had children under the age of 18 living with them, 44.1% were married couples living together, 13.3% had a female householder with no husband present, and 38.0% were non-families. 33.6% of all households were made up of individuals, and 14.3% had someone living alone who was 65 years of age or older. The average household size was 2.43 and the average family size was 3.13.

In the village, the population was spread out, with 21.5% under the age of 18, 7.4% from 18 to 24, 23.5% from 25 to 44, 26.8% from 45 to 64, and 20.8% who were 65 years of age or older. The median age was 44 years. For every 100 females there were 87.8 males. For every 100 females age 18 and over, there were 86.0 males.

The median income for a household in the village was $39,404, and the median income for a family was $54,375. Males had a median income of $35,806 versus $30,735 for females. The per capita income for the village was $19,408. About 2.9% of families and 6.3% of the population were below the poverty line, including 3.0% of those under age 18 and 17.0% of those age 65 or over.

Government
Oakwood was incorporated in 1951. In 1968 it enacted a home rule charter. The village is governed by a mayor-council form of government, with full-time services. Public safety services are provided by a full-time police department and a part-time fire department. The village also conducts its own mayor's court.

Notable person

 * Halle Berry, Academy Award-winning actress

title: Oakwood, Cuyahoga County, Ohio


text:
Olmsted Falls, Ohio

Olmsted Falls is a city in Cuyahoga County, Ohio, United States. The population was 8,582 at the 2020 census. A southwestern suburb of Cleveland, it is part of the Cleveland metropolitan area. The city's main business district is located at the corners of Bagley and Columbia Roads and contains the Grand Pacific Junction, a historic district.

History
After the Revolutionary War, the area that later became Olmsted Township, from which Olmsted Falls (as well as most of North Olmsted) was subsequently created, was part of the Western Reserve, a strip of northeastern Ohio land stretching 120 miles west from the Pennsylvania border, that was claimed by Connecticut. In 1795, Connecticut sold most of that land to the Connecticut Land Company, which then divided it into townships and sold it by auction. Several bidders won the right to purchase what then was known as Township 6, Range 15, with the largest share of almost half of the township going to Aaron Olmsted, a sea captain from East Hartford, Connecticut. However, it took years for the sales to be consummated. Olmsted died in 1806, so when the sale of his land was completed in 1807, it went to his widow and three sons, who sold parts of the land to settlers.

Although James Geer, who then lived in Columbia Township to the south, planted a crop of corn across the border in 1814, it was 1815 when he and his family moved into a small log house in Township 6, Range 15, to become the township’s first settlers in a section that later became part of Olmsted Falls. The township had several informal names, including Kingston, until 1823, when it was organized as a civil township called Lenox. However, because of confusion with another Lenox Township in Ashtabula County, one resident suggested renaming it Olmsted Township in honor of Aaron Olmsted. Olmsted’s son, Charles Hyde Olmsted, not only agreed to the request but was so pleased that he offered to send the community about 500 books from Connecticut by oxcart. Those books became known as the Oxcart Library.

On April 7, 1856, Olmsted Falls was incorporated as a village from a portion of Olmsted Township. In 1857, the village doubled in size when it annexed Plum Creek, the unincorporated hamlet to the north. Olmsted Falls subsequently annexed other parts of Olmsted Township over the years. In 1970, voters in Olmsted Falls and Westview (also known as West View) voted to merge their two villages, which were roughly the same size, under the name Olmsted Falls. The merger became effective at the beginning of 1971. In 1972, the state recognized Olmsted Falls as Ohio’s 231st city because it had a population of more than 5,000 people. The city is governed by a charter with a mayor and council elected on a non-partisan basis.

Two railroads run through Olmsted Falls. CSX tracks, originally built in 1849, cross northeast-southwest through the southeastern corner of the city. Norfolk Southern tracks, originally built in 1853, cut east-west through the city.

Olmsted Falls is part of the Olmsted Falls City School District, which also includes Olmsted Township and parts of Berea and Columbia Township.

Vitamix has its world headquarters in Olmsted Township right on the border with Olmsted Falls.

Geography
Olmsted Falls is located at 41.3675°N, -81.90472°W (41.367626, -81.904818). According to the United States Census Bureau, the city has a total area of 4.12 sqmi, all land.

2010 census
As of the census of 2010, there were 9,024 people, 3,684 households, and 2,431 families residing in the city. The population density was 2190.3 PD/sqmi. There were 3,897 housing units at an average density of 945.9 /sqmi. The racial makeup of the city was 94.9% White, 2.0% African American, 0.1% Native American, 1.2% Asian, 0.4% from other races, and 1.3% from two or more races. Hispanic or Latino of any race were 2.6% of the population.

There were 3,684 households, of which 32.6% had children under the age of 18 living with them, 52.5% were married couples living together, 11.0% had a female householder with no husband present, 2.6% had a male householder with no wife present, and 34.0% were non-families. 28.8% of all households were made up of individuals, and 9.4% had someone living alone who was 65 years of age or older. The average household size was 2.42 and the average family size was 3.01.

The median age in the city was 41.6 years. 24.5% of residents were under the age of 18; 6.7% were between the ages of 18 and 24; 24.1% were from 25 to 44; 31% were from 45 to 64; and 13.7% were 65 years of age or older. The gender makeup of the city was 46.7% male and 53.3% female.

2000 census
As of the census of 2000, there were 7,962 people, 3,121 households, and 2,228 families residing in the city. The population density was 1,927.2 PD/sqmi. There were 3,267 housing units at an average density of 790.8 /sqmi. The racial makeup of the city was 96.71% White, 1.31% African American, 0.99% Native American, 0.73% Asian, 0.06% Pacific Islander, 0.28% from other races, and 0.88% from two or more races. Hispanic or Latino of any race were 1.51% of the population. As of 2006, the population is estimated to be 10,000+.

There were 3,121 households, out of which 34.4% had children under the age of 18 living with them, 60.2% were married couples living together, 8.7% had a female householder with no husband present, and 28.6% were non-families. 24.8% of all households were made up of individuals, and 6.9% had someone living alone who was 65 years of age or older. The average household size was 2.54 and the average family size was 3.06.

In the city the population was spread out, with 26.6% under the age of 18, 6.2% from 18 to 24, 32.4% from 25 to 44, 24.9% from 45 to 64, and 9.9% who were 65 years of age or older. The median age was 37 years. For every 100 females, there were 92.8 males. For every 100 females age 18 and over, there were 89.2 males.

The median income for a household in the city was $57,826, and the median income for a family was $66,196. Males had a median income of $41,996 versus $35,110 for females. The per capita income for the city was $25,716. About 1.2% of families and 2.1% of the population were below the poverty line, including 1.2% of those under age 18 and 4.5% of those age 65 or over.

Executive
The mayor is the ceremonial head of government. The mayor is full-time and presides over city council meetings, has the power to veto council actions, and also acts as the Safety Director for the city.

James Patrick Graven was elected mayor on December 5, 2017 after receiving over 60% of the vote in a special runoff election. He was narrowly elected to a second term in November 2021.

Legislative
The City Council of Olmsted Falls consists of seven members elected to two year terms; Council President, Council President Pro-Tempore, Council-At-Large, Clerk of Council, representative for Ward 1, representative for Ward 2, representative for Ward 3, and representative for Ward 4. It is a "strong Council - weak Mayor" form of government, with the Mayor not holding any voting rights on Council.

The Current Olmsted Falls City Council as of January 2024 is: Cornel Munteanu, Council President; Brian Chitester, Council Pro-Tempore; Megan Coy, Council-At-Large; Jay McFadden, Council Ward 1; Sean Wolanin, Council Ward 2; Chad Gluss, Council Ward 3; Scott Saari, Council Ward 4

Judicial
The Mayor's Court of Olmsted Falls is located in the City Hall building.

Education
Olmsted Falls is served by the public Olmsted Falls City School District. There are five schools in the school system; Early Childhood Center, Falls-Lenox Primary School, Olmsted Falls Intermediate School, Olmsted Falls Middle School, and Olmsted Falls High School.

Notable people

 * Stetson Allie, Major League Baseball pitcher and outfielder
 * Mamie Colvin, temperance activist
 * Mike Gansey, professional basketball executive and former player who is currently the general manager for the Cleveland Cavaliers of the National Basketball Association
 * Steve Gansey, former basketball player and coach
 * Norb Hecker, American football player and coach who was part of eight National Football League championship teams
 * Lora Hirschberg, sound engineer
 * Mickey Mental, head football coach at Weber State University
 * Dan Monahan, actor
 * Katie Moon, Olympic pole vaulting gold medalist
 * Philip Yenyo, Native American civil rights activist
 * Sean Zawadzki, professional soccer player for the Columbus Crew in Major League Soccer

title: Olmsted Falls, Ohio


text:
Orange, Ohio

Orange is a village in eastern Cuyahoga County, Ohio, United States. The population was 3,421 at the 2020 census. An affluent eastern suburb of Cleveland, it is part of the Cleveland metropolitan area.

History
Orange Township was settled in 1815 and established as a township in 1820. As part of the settlement of the Connecticut Western Reserve, Serenus Bumett was the first settler in the township. The name "Orange" was chosen because several of the early settlers had migrated from Orange, Connecticut. In 1831, Orange Township was the birthplace of President James A. Garfield. However, since then, Orange Township has been divided into five parts. These are Orange Village, Hunting Valley, Moreland Hills, Pepper Pike and Woodmere. Garfield's birth and early childhood occurred in modern-day Moreland Hills.

Orange Village, the southwest quadrant of the original township, was incorporated as a village in 1929.

Geography
According to the United States Census Bureau, the village has a total area of 3.82 sqmi, of which 3.80 sqmi is land and 0.02 sqmi is water. The affluent village is the home of the scenic Beechmont Country Club golf course.

2010 census
As of the census of 2010, there were 3,323 people, 1,277 households, and 973 families living in the village. The population density was 874.5 PD/sqmi. There were 1,374 housing units at an average density of 361.6 /sqmi. The racial makeup of the village was 77.1% White, 14.4% African American, 0.1% Native American, 5.7% Asian, 0.1% Pacific Islander, 0.7% from other races, and 1.9% from two or more races. Hispanic or Latino of any race were 1.6% of the population.

There were 1,277 households, of which 33.4% had children under the age of 18 living with them, 64.1% were married couples living together, 8.6% had a female householder with no husband present, 3.4% had a male householder with no wife present, and 23.8% were non-families. 21.4% of all households were made up of individuals, and 10.9% had someone living alone who was 65 years of age or older. The average household size was 2.59 and the average family size was 3.03.

The median age in the village was 46.8 years. 24.8% of residents were under the age of 18; 5.3% were between the ages of 18 and 24; 17.8% were from 25 to 44; 34.1% were from 45 to 64; and 18.1% were 65 years of age or older. The gender makeup of the village was 48.1% male and 51.9% female.

2000 census
As of the census of 2000, there were 3,236 people, 1,170 households, and 959 families living in the village. The population density was 851.4 PD/sqmi. There were 1,236 housing units at an average density of 325.2 /sqmi. The racial makeup of the village was 81.46% White, 12.64% African American, 0.06% Native American, 4.20% Asian, 0.09% Pacific Islander, 0.25% from other races, and 1.30% from two or more races. Hispanic or Latino of any race were 0.71% of the population. 12.3% were of American, 9.1% Russian, 6.8% German, 6.4% Italian, 6.3% Hungarian, 5.7% English, and 1.1% Israeli ancestry according to Census 2000. 98.3% spoke English and 1.0% Hebrew as their first language.

There were 1,170 households, out of which 41.6% had children under the age of 18 living with them, 71.5% were married couples living together, 8.5% had a female householder with no husband present, and 18.0% were non-families. 16.3% of all households were made up of individuals, and 9.1% had someone living alone who was 65 years of age or older. The average household size was 2.75 and the average family size was 3.10.

In the village, the population was spread out, with 28.8% under the age of 18, 3.4% from 18 to 24, 21.8% from 25 to 44, 29.4% from 45 to 64, and 16.6% who were 65 years of age or older. The median age was 43 years. For every 100 females there were 97.1 males. For every 100 females age 18 and over, there were 89.9 males.

The median income for a household in the village was $89,660, and the median income for a family was $102,206. Males had a median income of $77,865 versus $37,667 for females. The per capita income for the village was $46,296. About 2.3% of families and 3.6% of the population were below the poverty line, including 5.2% of those under age 18 and 1.1% of those age 65 or over.

Schools
Orange Village is served by the Orange City School System.

title: Orange, Ohio


text:
Parma, Ohio

Parma is a city in Cuyahoga County, Ohio, United States, located on the southern edge of Cleveland. As of the 2020 census, its population was 81,144. Parma is the seventh largest city in the state of Ohio, the largest suburb in the state, and the second largest city in Cuyahoga County after Cleveland.

Greenbriar (1806–1826)
In 1806, the area that would eventually become Parma and Parma Heights was originally surveyed by Abraham Tappan, a surveyor for the Connecticut Land Company, and was known as Township 6 - Range 13. This designation gave the town its first identity in the Western Reserve. Soon after, Township 6 - Range 13 was commonly referred to as "Greenbriar", supposedly for the rambling bush that grew there. Benajah Fay, his wife Ruth Wilcox Fay, and their ten children, arrivals from Lewis County, New York, were the first settlers in 1816. It was then that Greenbriar, under a newly organized government seat under Brooklyn Township, began attending to its own governmental needs.

Parma Township (1826–1924)
Self-government started to gain in popularity by the time the new Greenbriar settlement contained twenty householders. However, prior to the establishment of the new township, the name Greenbriar was replaced by the name Parma. This was largely due to Dr. David Long who had recently returned from Italy and "impressed with the grandeur and beauty...was reminded of Parma, Italy and...persuaded the early townspeople that the territory deserved a better name than Greenbriar."

Thus, on March 7, 1826, a resolution was passed ordering the construction of the new township. It stated,

"On the petition of sundry inhabitants for a new township to be organized and erected comprising No. 6 in the 13th Range. Ordered that said Township No. 6 in the 13th Range be set off and erected into a new Township by the name of Parma, to be bounded by the original lines of said Township."

On the same day, a public notice was issued to qualified electors by the County Commissioners. They met at the Samuel Freeman House on April 3, 1826, to elect township officers according to the law. It was then that the first eleven officers were elected to lead the new government.

During this time, Parma Township remained largely agricultural. The first schoolhouse was a log structure built on the hill at the northern corner of what is now Parma Heights Cemetery. A memorial plate on a stone marks the spot. In 1827, the township was divided into road districts. The Broadview Road of today was then known as Town Line Road as well as Independence Road. Ridge Road was known then as Center Road as it cut through the center of town. York Road was then known as York Street as arrivals from the state of New York settled there. Pearl Road then had many names which included Medina Wooster Pike, Wooster Pike, the Cleveland Columbus Road, and the Brighton and Parma Plank Road.

A stone house, built in 1849 and known as the Henninger House, was occupied by several generations of Henningers and is still standing today. The house rests on one of the higher points in Cuyahoga County, which provided visibility for the entire northeastern part of Parma Township. This was also the same site where the Erie Indians, centuries before, stood to read and send fire signals as well as pray to their spirits.

By 1850, the US census listed Parma Township's population at 1,329. However, the rising population of the township had slowed over the decades. The Civil War affected Parma much as it did other towns and villages in the nation. Three out of four homes sent a father, sons, or sometimes both, to fight in the war. By 1910, the population of the township had increased to 1,631.

In 1911, Parma Heights, due to the temperance mood of the day, separated itself from the Parma Township after by a vote of 42 to 32 and was incorporated as a village comprising 4.13 square miles.

 * "A main reason for establishing the village of Parma Heights was to get a town marshal...There is one saloon in the territory...some pretty rough crowds Sundays have disturbed the quiet of the neighborhood...wanted it closed on Sundays. To do this they wished a town marshal. They couldn't have a town marshal without becoming a village, so they became one."

The Village of Parma (1924–1930)
By 1920, the US census showed Parma Township had a population of just 2,345, but the following decade proved to be a time of significant growth and development for Parma. It was in the 1920s that Parma Township transformed from a farming community into a village. On December 15, 1924, Parma was incorporated as a village.

The largest and fastest growing development of that time was H. A. Stahl's Ridgewood Gardens development, which started in 1919, continued through the 1920s, and into the 1930s. A resident of Shaker Heights, Ohio's first Garden City, H. A. Stahl developed Ridgewood as an ambitious "model village" project patterned along the lines of and rivaling the earlier Shaker Heights project with "churches, schools, motion picture theater, community house, and other features forming a part of all well-developed residence communities". Ridgewood was designed and marketed as a Garden City on 1,000 acres of land to accommodate about 40,000 residents "325 feet above Lake Erie, in the healthiest section of the South Side, free from the smoke of industries, or the congestion and noises of sections nearer the Public Square."

The City of Parma (1931–present)
On January 1, 1931, Parma became a city with a population of 13,899. Whereas the incorporation of the village of Parma was met with much optimism, the newly established city of Parma faced the uncertainty of the Great Depression which had almost entirely stopped its growth. Money was scarce, tax income was limited, and some began to talk of annexation of both the city and school district to Cleveland. Both annexation issues, however, were soundly defeated as Parma voters overwhelmingly voted against them and silenced proponents of annexation. Not long after this, Parma was once again solvent due in large part to the newly created Gallagher Act, a 1936 Ohio law that aided cities threatened with bankruptcy and the determination of Parma's Auditor, Sam Nowlin. By 1941, a building boom appeared to be underway in Parma just as the United States was about to enter World War II.

After World War II, Parma once again began to experience tremendous growth as young families began moving from Cleveland into the suburbs. Between 1950 and 1960, Parma's population soared from 28,897 to 82,845. By 1956, Parma was unchallenged as the fastest growing city in the United States. The population peaked in 1970 at 100,216.

In 2016, Parma's population had declined to 81,601, though it remains one of the Cleveland area's top three destinations young adults (aged 22 to 34) are increasingly choosing as a place to live, along with Lakewood and downtown Cleveland and in 2016 was recognized by Businessweek as one of the best places to raise kids in Ohio.

Geography
Parma is southwest of Cleveland; it is bounded by Cleveland and Brooklyn on the north, Brooklyn Heights, and Seven Hills on the east, North Royalton and Broadview Heights on the south, and Brook Park, Middleburg Heights, and Parma Heights on the west.

According to the United States Census Bureau, the city has a total area of 20.07 sqmi, of which 20.02 sqmi is land and 0.05 sqmi is water.

Two major changes and developments have recently occurred regarding two principal sites within the city:
 * 1) The West Creek Preservation Agency has worked to preserve various historic and natural sites in the city, including the Henninger House and the West Creek Watershed.
 * 2) Henninger House, built in 1849 and the oldest standing home in Parma, is planned to be part of the proposed Quarry Creek Historic District.

Surrounding communities
Parma is bounded by Cleveland and Brooklyn on the north, Brooklyn Heights, and Seven Hills on the east, North Royalton and Broadview Heights on the south, and Brook Park, Middleburg Heights, and Parma Heights on the west.

2020 census
According to the 2020 United States census, Parma had a population of 81,146. Of which, 82.3% were non-Hispanic White, 6.8% were Hispanic/Latino, 4.0% were non-Hispanic Black, 2.5% were Asian, 4.4% were mixed or other.

2010 census
As of the 2010 United States Census, there were 81,601 people, 34,489 households, and 21,646 families residing in the city. The population density was 4076.0 PD/sqmi. There were 36,608 housing units at an average density of 1828.6 /sqmi. The racial makeup of the city was 93.0% White, 2.3% African American, 0.2% Native American, 1.9% Asian, 1.0% from other races, and 1.6% from two or more races. Hispanic or Latino of any race were 3.6% of the population. According to the 2010 Census., 22.5% were of German ancestry, 17.6% Polish, 14.8% Italian, 13.8% Irish, 7.4% Slovak, 6.7% English, 5.3% Ukrainian, 2.6% French, 2.2% Serbian, 1.9% Czech, 1.4% Arab, and 1.2% of Croatian, Lithuanian, or Russian ancestries. In regard to languages spoken, 87.03% spoke English, 2.26% Ukrainian, 1.68% Polish, 1.27% Spanish, 1.24% German, and 1.18% Italian as their first language.

There were 34,489 households, of which 27.1% had children under the age of 18 living with them, 45.7% were married couples living together, 12.4% had a female householder with no husband present, 4.6% had a male householder with no wife present, and 37.2% were non-families. 31.8% of all households were made up of individuals, and 12.9% had someone living alone who was 65 years of age or older. The average household size was 2.34 and the average family size was 2.95.

The median age in the city was 41.5 years. 20.4% of residents were under the age of 18; 8.5% were between the ages of 18 and 24; 25.7% were from 25 to 44; 27.7% were from 45 to 64; and 17.7% were 65 years of age or older. The gender makeup of the city was 48.1% male and 51.9% female.

Income
The median income for a household in the city was $50,198, the median income for a family was $60,696 and the mean income for a family was $68,828. The per capita income for the city was $25,064. The poverty rate in the city was 10.2%. This was low in comparison to other large Ohio cities as well as the state's individual poverty rate of 15.4%.

Safety
In 2014, Parma ranked as the third safest city in the United States with a population of 25,000 or more by Neighborhood Scout. In 2014, Parma had a crime index of 90 meaning it was safer than 90% of cities in the United States.

Economy
During the population boom between 1950 and 1980, Parma's commercial sector grew to match its residential sector. Since the 1950s, Parma has fostered the growth of many small businesses and been an operating hub for companies including General Motors, Cox Cable, and formerly, the Union Carbide Research Center.

The Shoppes at Parma
The Shoppes at Parma, formerly Parmatown Mall, is a commercial shopping district that totals approximately 800,000 square feet. It is located approximately 3 miles south of Cleveland's southern border at the southwest corner of Ridge Road and West Ridgewood Drive in central Cuyahoga County. It is anchored by J.C. Penney, Dick's Sporting Goods, Marc's and Walmart. The mall opened as a shopping plaza in 1956 and was enclosed in the mid-1960s.

Currently, it is owned and managed by Phillip's Edison & Co. and is undergoing extensive redevelopment at an expected cost of more than $70 million.

Redevelopment will transform the commercial center into a pedestrian-friendly community-oriented mall and will include attractive landscaping, new lighting, creation of two tree-lined boulevards, repaving of the parking lots, changing the entire facade of the outdoor shopping strip and medical offices, demolition of the current Macy's and Dick's Sporting Goods buildings, creating a new point of entry to J.C. Penney from West Ridgewood Drive, the construction of six new outbuildings, and the separation of Walmart from the rest of the mall.

In January 2014, it was announced that a 15-member "Parma Mayor's Town Center Task Force" will be formed to develop a plan for a town center based around the Ridge Road-West Ridgewood Drive intersection that features the Shoppes at Parma, Parma Branch library, University Hospitals Parma Medical Center and City Hall. It will be made up of representatives from various organizations including the Cuyahoga County Public Library, Parma Area Chamber of Commerce, Parma schools and the Cleveland Metroparks' West Creek Reservation.

Ukrainian Village
The Ukrainian Village commercial district is located along State Road between Tuxedo Avenue and Grantwood Drive. This district was designated Ukrainian Village in September 2009.

This commercial district features a large number of small, family-owned businesses and medical offices, features one of the most "walkable" neighborhoods in Parma, and boasts a traffic count of more than 40,000 vehicles each day at the intersection of State and Snow Roads. This area also hosts the Ukrainian Independence Day parade (August).

In 2013, Parma formed a sister-city relationship with Lviv, Ukraine and is home to Ohio's largest Ukrainian community, the majority of whom are foreign born, with more than twice the number of any other city.

Parma is the seat of the Ukrainian Catholic Eparchy of Saint Josaphat, which was established by Pope John Paul II in 1983.

Polish Village
The Polish Village commercial district is located along Ridge Road between Pearl Road and Thornton Avenue. This district was designated Polish Village on May 1, 2011.

This commercial district features a large number of small, family-owned businesses and medical offices, features one of the most walkable neighborhoods in Parma, and boasts a traffic count of more than 40,000 vehicles each day at the intersection of Ridge and Snow Roads. This area also hosts the Polish Constitution Day parade (May), St. Charles Carnival parade (July), Independence Day parade (July), and Christmas parade (December).

Public schools
The Parma City School District serves Parma, Parma Heights and Seven Hills. The District's sports stadium is Byers Field. All three high schools play golf at Ridgewood for their home course. The rivalry that exists between these schools is well documented.

Elementary schools

 * Dentzler Elementary School
 * Green Valley Elementary School
 * John Muir Elementary School
 * Pleasant Valley Elementary School
 * Ridge-Brook Elementary School
 * Thoreau Park Elementary School

Middle schools

 * Greenbriar Middle School
 * Shiloh Middle School
 * Hillside Middle School

High Schools

 * Normandy High School
 * Valley Forge High School
 * Parma Senior High School (1953-2023)

Charter schools
Constellation Schools: Parma Community public charter schools:

Elementary schools

 * Parma Community Elementary

Middle schools

 * Parma Community Middle

High schools

 * Parma Community High

Elementary/middle schools

 * Al Ihsan School Elementary (K-5)
 * Bethany Lutheran School (PK-8)
 * Bethel Christian Academy (PK-8)
 * Holy Family School (PK-8)
 * St. Anthony of Padua Elementary School (K-8)
 * St. Bridget School (PK-8)
 * St. Charles Borromeo Parish School (PK-8)
 * St. Columbkille Parish School (PK-8)

High schools

 * Padua Franciscan (9–12)

Colleges

 * Bryant & Stratton College
 * Cuyahoga Community College Western Campus

Transportation
Parma's major north–south roads, in order from west to east, are:
 * West 130th Street, which forms part of the western border of Parma,
 * Chevrolet Boulevard/Stumph Road/York Road,
 * Ridge Road (State Route 3),
 * West 54th Street
 * State Road (State Route 94),
 * Broadview Road (State Route 176), which forms part of the eastern boundary of Parma. The State Route 176 designation continues northward via the Jennings Freeway, connecting Parma to downtown Cleveland.

Its major east–west roads, in order from north to south, are:
 * I-480, running just north of Parma's northern border,
 * Brookpark Road (State Route 17), forming Parma's northern border with Cleveland,
 * Snow Road,
 * West Ridgewood Drive,
 * West Pleasant Valley Road, and
 * Sprague Road, which forms the southern border of Parma.

Also, Pearl Road (U.S. Route 42) runs from southwest to northeast through northern Parma for less than two miles (3 km).

The speed limit is 35 mph on most major thoroughfares in Parma. The exception is in business zones which have 25 mph speed limit.

Public transportation in Parma includes bus routes operated by the Greater Cleveland Regional Transit Authority, which serves the city of Cleveland and Cuyahoga County suburbs.

Notable people

 * Bill Balas, screenwriter, director and producer
 * Jeremiah Wallace Baldock, Wisconsin State Assemblyman
 * Michael Bierut, graphic designer
 * Hector Boiardi, better known as Chef Boyardee, died in Parma in 1985.
 * Shya Chitaley, Curator of paleobotany at the Cleveland Museum of Natural History
 * Carmen Cozza, football coach at Yale University.
 * Timothy DeGeeter, state representative
 * Dan Fritsche, NHL player, Minnesota Wild, Columbus Blue Jackets and New York Rangers
 * Erich Gliebe, CEO of the white supremacist National Alliance, also professional boxer
 * Michael T. Good, NASA astronaut
 * Brian Holzinger, NHL, Buffalo Sabres
 * James Hoye, umpire in Major League Baseball
 * Dan Huberty, Republican member of the Texas House of Representatives
 * Scott Jarvis, actor
 * William Kowalski, author and educator
 * Ted Levine, actor
 * James A. Lovell, NASA Astronaut (Gemini 7, Gemini 12, Apollo 8 and Apollo 13 missions)
 * Biagio Messina, television producer, filmmaker, and actor.
 * Mike Mizanin, actor and professional wrestler known under the ring name The Miz
 * Clint Nageotte, professional baseball player
 * Alex Nedeljkovic, goaltender for the Pittsburgh Penguins of the NHL.
 * Ransom E. Olds, automotive pioneer
 * Benjamin Orr (Orzechowski), best known as co-lead singer and bassist for The Cars.
 * Kermit Poling, conductor, violinist and composer; music director of the South Arkansas Symphony; concertmaster of the Shreveport Symphony Orchestra
 * Frank Romano, guitarist, songwriter and record producer
 * Alan Ruck, actor (Ferris Bueller's Day Off, Spin City)

Moon Over Parma
In the late 1980s, Bob McGuire penned a song entitled "Moon Over Parma", about an eccentric courtship that traverses the various suburbs of Cleveland. The song first received wide exposure on Big Chuck and Lil' John during its "New Talent Time" segment. Though McGuire was given the shepherd's crook, McGuire's song was offered for free, in the form of sheet music, to those who wrote to the show requesting a copy.

The Drew Carey Show’s opening credits of its first season consisted of a caricature of Drew Carey — consisting of his face and a yellow tie — singing "Moon Over Parma" with an abridgment and some minor lyrical changes.

Parma Place
Occasionally, during the 1960s and 1970s, Parma was the target of light-hearted jabs by local movie show hosts Ghoulardi, Hoolihan, Big Chuck and Lil’ John, and The Ghoul, due to its central European image promoted by the friendly rivalry between Ernie "Ghoulardi" Anderson and "Big Chuck" Schodowski and contrary to actual demographics. Ghoulardi, the horror host of late night Shock Theater at WJW-TV, Channel 8, in Cleveland from January 13, 1963, through December 16, 1966, made a series of shorts called "Parma Place" and focused on an alleged love of white socks, pink flamingos, chrome balls, kielbasa, pierogi and the polka.

Novak v. City of Parma
In March 2016, Anthony Novak, a resident of Parma, created a parody Facebook page superficially resembling the local police department's official page, with outlandish, satirical posts easily distinguished from actual police public-affairs content. Despite the page being voluntarily removed after 12 hours, the Parma Police subsequently obtained warrants and raided Novak's apartment in the middle of the night three weeks later, seizing electronic devices belonging Novak and his roommate, and arresting and jailing Novak for four days until he could make bail. Novak was charged with felony disruption of police operations, but was acquitted at trial; a subsequent lawsuit against the police for civil rights violations was rebuffed by the Sixth Circuit, citing qualified immunity. Novak's appeal to the U.S. Supreme Court garnered legal briefs from the ACLU and Cato Institute, but gained notoriety because of a supporting brief filed by satirical website The Onion.

title: Parma, Ohio


text:
Parma Heights, Ohio

Parma Heights is a city in Cuyahoga County, Ohio, United States. The city's population was 20,863 as of the 2020 census. A suburb of Cleveland, it is a part of the Cleveland metropolitan area. Parma Heights is surrounded on the north, east and south by the larger city of Parma. The cities of Brook Park and Middleburg Heights form most of the western border.

"Greenbriar" (1806–1826)
In 1806, the area that was to become Parma and Parma Heights was originally surveyed by Abraham Tappan, a surveyor for the Connecticut Land Company, and was known as Township 6 - Range 13. This designation gave the town its first identity in the Western Reserve. Soon after, Township 6 - Range 13 was commonly referred to as "Greenbriar," supposedly for the rambling bush that grew there. Benajah Fay, his wife Ruth Wilcox Fay, and their ten children, arrivals from Lewis County, New York, were the first settlers in 1816. The area of Greenbriar that was to later become Parma Heights was first settled in 1817. It was around that time that Greenbriar, under a newly organized government seat under Brooklyn Township, began attending to its own governmental needs.

Parma Township (1826–1911)
Self-government started to gain in popularity by the time the new Greenbriar settlement contained twenty householders. However, prior to the establishment of the new township, the name Greenbriar was replaced by the name Parma. This was largely due to Dr. David Long who had recently returned from Italy and "impressed with the grandeur and beauty...was reminded of Parma, Italy and...persuaded the early townspeople that the territory deserved a better name than Greenbriar."

Thus, on March 7, 1826, a resolution was passed ordering the construction of the new township. It stated,

 * "On the petition of sundry inhabitants for a new township to be organized and erected comprising No. 6 in the 13th Range. Ordered that said Township No. 6 in the 13th Range be set off and erected into a new Township by the name of Parma, to be bounded by the original lines of said Township."

On the same day, a public notice was issued to qualified electors by the County Commissioners. They met at the house of Samuel Freeman on April 3, 1826 to elect township officers according to the law. It was then that the first eleven officers were elected to lead the new government.

During this time, Parma Township remained largely agricultural. The first schoolhouse was a log structure built on the hill at the northern corner of what is now Parma Heights Cemetery. A memorial plate on a stone marks the spot. In 1827, the township was divided into road districts. The Broadview Road of today was then known as Town Line Road as well as Independence Road. Ridge Road was known then as Center Road as it cut through the center of town. York Road was then known as York Street as arrivals from the state of New York settled there. Pearl Road then had many names which included Medina Wooster Pike, Wooster Pike, the Cleveland Columbus Road, and the Brighton and Parma Plank Road.

A stone house, known as the Henninger House, was built in 1849, occupied by several generations of Henningers, and is still standing today. More than 160 years ago, this house rested on one of the highest points in Cuyahoga County which provided visibility for the entire northeastern part of Parma Township. This was also the same site that the Erie Indians, centuries before, also stood to read and send fire signals as well as pray to their spirits.

By 1850, the US census listed Parma Township's population at 1,329. However, the rising population of the township had slowed over the decades. The Civil War affected Parma much like it did other towns and villages in the nation. Three out of four homes sent father or sons, or sometimes both, to fight in the war. By 1910, the population of the township had increased to 1,631.

Village of Parma Heights (1911–1956)
In 1911, Parma Heights, due to the temperance mood of the day, separated itself from the Parma Township by a vote of 42 to 32 and was incorporated as a village comprising 4.13 square miles.

 * "A main reason for establishing the village of Parma Heights was to get a town marshal...There is one saloon in the territory...some pretty rough crowds Sundays have disturbed the quiet of the neighborhood...wanted it closed on Sundays...To do this they wished a town marshal. They couldn't have a town marshal without becoming a village, so they became one."

By 1920, census records show that Parma Heights contained 310 residents.

City of Parma Heights (1956-Present)
In December 1956, Parma Heights was incorporated as a city, under the administration of Roy F. Cappallo, Mayor.

On November 26, 2014, an early-morning fire destroyed the office of Mayor Mike Byrne and resulted in severe damage to city hall. Investigators determined the fire was intentionally set using a Molotov cocktail.

Geography
Parma Heights is located at 41.38611°N, -81.76333°W (41.386051, -81.763459).

According to the United States Census Bureau, the city has a total area of 4.19 sqmi, all land.

Languages
88.5% spoke English, 1.4% Ukrainian, 1.3% Spanish, 1.3% Polish, 1.2% Romanian, 1.2% Italian, and 0.9% German and Hungarian.

2010 census
As of the 2010 United States Census, there were 20,718 people, 9,534 households, and 5,298 families residing in the city. The population density was 4944.6 PD/sqmi. There were 10,295 housing units at an average density of 2457.0 /sqmi. The racial makeup of the city was 91.1% White, 2.8% African American, 0.2% Native American, 3.0% Asian, 1.0% from other races, and 1.8% from two or more races. Hispanic or Latino of any race were 3.8% of the population.

There were 9,534 households, of which 23.4% had children under the age of 18 living with them, 39.7% were married couples living together, 11.7% had a female householder with no husband present, 4.2% had a male householder with no wife present, and 44.4% were non-families. 39.1% of all households were made up of individuals, and 18.6% had someone living alone who was 65 years of age or older. The average household size was 2.15 and the average family size was 2.89.

The median age in the city was 43.2 years. 18.9% of residents were under the age of 18; 8.2% were between the ages of 18 and 24; 24.9% were from 25 to 44; 27.6% were from 45 to 64; and 20.5% were 65 years of age or older. The gender makeup of the city was 46.5% male and 53.5% female.

2000 census
As of the 2000 United States Census, there were 21,659 people, 9,823 households, and 5,825 families residing in the city. The population density was 5,158.6 PD/sqmi. There were 10,263 housing units at an average density of 2,444.4 /sqmi. The racial makeup of the city was 94.76% White, 1.17% African American, 0.13% Native American, 2.33% Asian, 0.01% Pacific Islander, 0.45% from other races, and 1.15% from two or more races. Hispanic or Latino of any race were 1.62% of the population.

There were 9,823 households, out of which 22.6% had children under the age of 18 living with them, 46.0% were married couples living together, 9.9% had a female householder with no husband present, and 40.7% were non-families. 36.5% of all households were made up of individuals, and 20.2% had someone living alone who was 65 years of age or older. The average household size was 2.18 and the average family size was 2.86.

In the city the population was spread out, with 19.1% under the age of 18, 7.2% from 18 to 24, 27.5% from 25 to 44, 21.1% from 45 to 64, and 25.1% who were 65 years of age or older. The median age was 42 years. For every 100 females, there were 86.0 males. For every 100 females age 18 and over, there were 81.9 males.

The median income for a household in the city was $36,985, and the median income for a family was $48,641. Males had a median income of $39,034 versus $27,564 for females. The per capita income for the city was $20,522. About 5.4% of families and 7.6% of the population were below the poverty line, including 10.7% of those under age 18 and 7.0% of those age 65 or over.

Government
There are seven council members serving at large. Every two years there is an election. Four positions are open. The top three candidates are each elected for a four-year term. The fourth candidate is awarded a two-year term.

The current mayor of Parma Heights is former city council member Marie Gallo, who beat fellow council member Anthony Stavole in a landslide election in November 2021. Gallo was sworn into office on January 1, 2022.

Education
Parma Heights is included in the Parma City School District. Parma Park Elementary School (grades K–4) and Valley Forge High School (grades 9–12) are located within the city limits. Private schools include Holy Name High School, Holy Family School, Incarnate Word Academy, and Parma Heights Christian Academy.

Parma Heights is home to the Western Campus of Cuyahoga Community College.

title: Parma Heights, Ohio