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Samuel Rinnah Van Sant

Samuel Rinnah Van Sant (May 11, 1844 – October 3, 1936) was an American politician who served in the Minnesota House of Representatives and as the 15th Governor of Minnesota.

Early life
Van Sant was born in Rock Island, Illinois, to John Wesley Van Sant and Lydia Van Sant (née Anderson). His family had a long history in the shipbuilding industry and his father worked with building and repairing steamboats on the Mississippi River. Van Sant attended school in Rock Island. When the American Civil War began, he attempted to enlist but was rejected as too young. After getting written permission from his father, Van Sant was accepted and served with the 9th Regiment Illinois Volunteer Cavalry for three years before being mustered out.

After the war, Van Sant took business classes in Hudson, New York, and briefly attended Knox College in Illinois before leaving school due to a lack of money. He worked with his father in the shipbuilding trade and helped develop specialized raft boats for moving lumber along the river. In 1883, he relocated to Winona, Minnesota.

Career
After arriving in Winona, Van Sant continued to work in the shipbuilding and lumber rafting industries. By the 1890s, he had become financially successful and his company was responsible for moving more lumber down the Mississippi River than any other.

He also became active with local Republican politics. In 1892, he was elected to the Minnesota House of Representatives and served two consecutive terms from 1893 to 1897. In his second term, he served as the Speaker of the House.

In 1900, he ran for governor against incumbent John Lind and won, serving two terms, from 1901 to 1905. As governor, Van Sant filed a lawsuit against the Northern Securities Company railroad trust arguing that its formation violated a state law. His case was later taken up at the federal level by President Theodore Roosevelt and, in the 1904 United States Supreme court case Northern Securities Co. v. United States, the company was dissolved. He was also involved in legislation which updated the state's election process and removed restrictions on the state legislature's taxation and spending powers.

After serving as Governor Van Sant retired from politics. He was commander in chief of the Grand Army of the Republic from 1909 to 1910.

He died in 1936 in Attica, Indiana, age 92. He is buried in Glendale Cemetery in Le Claire, Iowa.

The Samuel Van Sant House in Le Claire, Iowa is listed on the National Register of Historic Places.

title: Samuel Rinnah Van Sant


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Hypotenuse

In geometry, a hypotenuse is the side of a right triangle opposite the right angle. It is the longest side of any such triangle; the two other shorter sides of such a triangle are called catheti or legs. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two legs. Mathematically, this can be written as $$a^2 + b^2 = c^2$$, where a is the length of one leg, b is the length of another leg, and c is the length of the hypotenuse.

For example, if one of the legs of a right angle has a length of 3 and the other has a length of 4, then their squares add up to 25 = 9 + 16 = 3 × 3 + 4 × 4. Since 25 is the square of the hypotenuse, the length of the hypotenuse is the square root of 25, that is, 5. In other words, if $$a = 3$$ and $$b = 4$$, then $$c = \sqrt{a^2 + b^2} = 5$$.

Etymology
The word hypotenuse is derived from Greek ἡ τὴν ὀρθὴν γωνίαν ὑποτείνουσα (sc. γραμμή or πλευρά), meaning "[side] subtending the right angle" (Apollodorus), ὑποτείνουσα hupoteinousa being the feminine present active participle of the verb ὑποτείνω hupo-teinō "to stretch below, to subtend", from τείνω teinō "to stretch, extend". The nominalised participle, ἡ ὑποτείνουσα, was used for the hypotenuse of a triangle in the 4th century BCE (attested in Plato, Timaeus 54d). The Greek term was loaned into Late Latin, as hypotēnūsa. The spelling in -e, as hypotenuse, is French in origin (Estienne de La Roche 1520).

Properties and calculations
In a right triangle, the hypotenuse is the side that is opposite the right angle, while the other two sides are called the catheti or legs. The length of the hypotenuse can be calculated using the square root function implied by the Pythagorean theorem. It states that the sum of the two legs squared equals the hypotenuse squared. In mathematical notation, with the respective legs labelled a and b, and the hypotenuse labelled c, it is written as $$a^2 + b^2 = c^2$$. Using the square root function on both sides of the equation, it follows that
 * $$c = \sqrt { a^2 + b^2 } .$$

As a consequence of the Pythagorean theorem, the hypotenuse is the longest side of any right triangle; that is, the hypotenuse is longer than either of the triangle's legs. For example, given the length of the legs a = 5 and b = 12, then the sum of the legs squared is (5 × 5) + (12 × 12) = 169, the square of the hypotenuse. The length of the hypotenuse is thus the square root of 169, denoted $$\sqrt{169}$$, which equals 13.

The Pythagorean theorem, and hence this length, can also be derived from the law of cosines in trigonometry. In a right triangle, the cosine of an angle is the ratio of the leg adjacent of the angle and the hypotenuse. For a right angle γ (gamma), where the adjacent leg equals 0, the cosine of γ also equals 0. The law of cosines formulates that $$c^2 = a^2 + b^2 - 2ab\cos\theta$$ holds for some angle θ (theta). By observing that the angle opposite the hypotenuse is right and noting that its cosine is 0, so in this case θ = γ = 90°:

 * $$c^2 = a^2 + b^2 - 2ab\cos\theta = a^2 + b^2 \implies c = \sqrt{a^2 + b^2}.$$

Many computer languages support the ISO C standard function hypot(x,y), which returns the value above. The function is designed not to fail where the straightforward calculation might overflow or underflow and can be slightly more accurate and sometimes significantly slower.

Some languages have extended the definition to higher dimensions. For example, C++17 supports $$\mbox{std::hypot}(x, y, z) = \sqrt{x^2 +y^2 + z^2}$$; this gives the length of the diagonal of a rectangular cuboid with edges x, y, and z. Python 3.8 extended $$\mbox{math.hypot}$$ to handle an arbitrary number of arguments.

Some scientific calculators provide a function to convert from rectangular coordinates to polar coordinates. This gives both the length of the hypotenuse and the angle the hypotenuse makes with the base line (c1 above) at the same time when given x and y. The angle returned is normally given by atan2(y,x).

Trigonometric ratios
By means of trigonometric ratios, one can obtain the value of two acute angles, $$\alpha\,$$and $$ \beta\,$$, of the right triangle.

Given the length of the hypotenuse $$ c\,$$and of a cathetus $$ b\,$$, the ratio is:

 * $$ \frac{b}{c} = \sin (\beta)\,$$

The trigonometric inverse function is:

 * $$ \beta\ = \arcsin\left(\frac {b}{c} \right)\,$$

in which $$\beta\,$$ is the angle opposite the cathetus $$ b\,$$.

The adjacent angle of the catheti $$ b\,$$ is $$\alpha\,$$ = 90° – $$\beta\,$$

One may also obtain the value of the angle $$\beta\,$$by the equation:

 * $$ \beta\ = \arccos\left(\frac {a}{c} \right)\,$$

in which $$ a\,$$ is the other cathetus.

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

title: Hypotenuse


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John Albert Johnson

John Albert Johnson (July 28, 1861 – September 21, 1909) was an American politician. He served in the Minnesota State Senate from January 1897 to January 1901. He was the 16th governor of Minnesota from January 4, 1905, until his death on September 21, 1909 as a member of the Democratic Party.

Johnson was the first Minnesota governor born in Minnesota. He was only the second non-Republican governor in 45 years and the third since statehood. He was also first to serve a full term in the present state capitol, and the first to die in office. Johnson sought the 1908 Democratic presidential nomination but lost to William Jennings Bryan.

Biography
John Albert Johnson was born on a farm near St. Peter, Minnesota, on July 28, 1861, the eldest child of Gustaf and Caroline Johnson. After Gustaf abandoned his family, John left school at 13 to support his mother and siblings. During this time, he worked at a local drugstore. After that, he had a seven-year-long stint in the Minnesota National guard, where he reached the rank of captain. Local Democrats, impressed with the enterprising young store clerk, asked him to join their party and edit the strongly Democratic St. Peter Herald. Before he could take the position, he became seriously ill with typhoid fever, but he recovered. His journalistic success attracted statewide attention and fostered political aspirations.

Johnson married Elinor M. Preston on June 1, 1894, at the Union Presbyterian Church in St. Peter.

Johnson failed in early campaigns for state office from his heavily Republican home county but was elected to the state senate in 1898, indicating his growing bipartisan appeal.

Governor
In his 1904 inauguration speech, Johnson called for the two-year term to be extended to four years, more funding for roads, more funding to rural schools, and several other important ideas. Johnson's ability to reason and work with legislators of both parties resulted in such reform legislation as a reorganization of the state's insurance department to the benefit of policyholders, reduction of railroad passenger and freight rates, and removal of constitutional restraints on the legislature's power to tax.

Johnson was reelected in 1906 and 1908. He began his third term with reservations. At that point, he had had over four surgeries for his intestinal problems, and he wanted to pursue a promising sideline as a public orator. This chronic illness forced him to head to the Mayo Clinic once again on September 13, 1909. When he died suddenly at age 48 from post-operative complications, which included an infection, the state's citizens were grief-stricken.

Legacy
Johnson was the first of three governors to die in office. Governor Winfield Scott Hammond was the second, after suffering a stroke in 1915. Floyd B. Olson was the third and most recent, dying of cancer in 1936.

Statues of Johnson are on the steps of the Minnesota State Capitol and the grounds of the Nicollet County Courthouse. Johnson Senior High School in St. Paul is named for him, as is the portion of U.S. Route 169 from Saint Peter to the Twin Cities.

The John A. Johnson School in Virginia, Minnesota was built in 1907.

title: John Albert Johnson


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Adolph Olson Eberhart

Adolph Olson Eberhart (June 30, 1870 – December 6, 1944) was an American politician, who served as the 17th Governor of Minnesota.

Background
Adolph Olson Eberhart was born in Kil, in Värmland, Sweden, the son of Andrew and Louise Olson. Because of bad economic conditions, Andrew, Louise and all of the family except Adolph immigrated to St. Peter, Minnesota. In 1882, Adolph joined the family there. Eberhart graduated from Gustavus Adolphus College, St. Peter, Minnesota (1895) and studied law in a law office in Mankato, Minnesota.

Career
Eberhart was a member of the Minnesota State Senate from January 1903 to January 1907. He was elected the 17th Lieutenant Governor in 1906. He became the 17th Governor of Minnesota on September 21, 1909, when Governor John Albert Johnson died, and served until January 5, 1915. Eberhart was a Republican. Minnesota elected Governors and Lt. Governors on separate ballots until 1974, so it happened occasionally that the two were of different parties. Elected the youngest member of the state senate in 1902, the Republican Eberhart was chosen as lieutenant governor four years later in the administration of the legendary Democrat, John Albert Johnson. Although his first partial term as governor resulted from Johnson's death in 1909, he subsequently won the office twice on his own merits.

An efficient administrator, Eberhart was also a consummate politician, and his detractors, including many Republicans, questioned his sincerity as well as the reputation of certain close associates. To assure his re-nomination in 1912, he called a special 13-day legislative session and deflated his critics by bulldozing through such progressive reforms as rural school consolidation and primary elections. Eberhart's strategy worked; he avoided the censure of his own party and was re-nominated for a second full term in the first statewide primary.

Eberhart lost his re-nomination bid for a fourth term as governor. A second defeat in the 1916 U.S. Senate primary marked the end of his political career. After a career as a real estate and insurance executive in Chicago, he retired to a rest home where he died in Savage, Minnesota. An inventory of his gubernatorial records is maintained at the Minnesota Historical Society Library.

title: Adolph Olson Eberhart