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Frederick Buechner

Carl Frederick Buechner (July 11, 1926 – August 15, 2022) was an American author, Presbyterian minister, preacher, and theologian. The author of thirty-nine published books, his career spanned more than six decades and encompassed many different genres. He wrote novels, including Godric (1981 Pulitzer Prize finalist), A Long Day's Dying and The Book of Bebb, his memoirs, including The Sacred Journey, and theological works, such as Secrets in the Dark, The Magnificent Defeat, and Telling the Truth.

Buechner was named "without question one of the truly great writers of the 20th century" by viaLibri, a "major talent" by The New York Times, and "one of our most original storytellers" by USA Today. Annie Dillard (Pulitzer Prize-winning author of Pilgrim at Tinker Creek) called him "one of our finest writers." Buechner's works have been compared to C.S. Lewis and G.K. Chesterton and have been translated into twenty-seven languages.

Buechner was a finalist for the National Book Award, presented by the National Book Foundation, and has been awarded eight honorary degrees from such institutions as Yale University and the Virginia Theological Seminary. In addition, Buechner was the recipient of the O. Henry Award, the Rosenthal Award, the Christianity and Literature Belles Lettres Prize, and was recognized by the American Academy and Institute of Arts and Letters.

Early life
Carl Frederick Buechner, the eldest son of Katherine Golay (Kuhn) and Carl Frederick Buechner Sr., was born on July 11, 1926, in New York City. During Buechner's early childhood the family moved frequently, as Buechner's father searched for work. In The Sacred Journey, Buechner recalls that "Virtually every year of my life until I was fourteen, I lived in a different place, had different people to take care of me, went to a different school. The only house that remained constant was the one where my maternal grandparents lived in a suburb of Pittsburgh called East Liberty ... Apart from that one house on Woodland Road, home was not a place to me when I was a child. It was people." This changed in 1936, when Buechner's father committed suicide by carbon monoxide poisoning, a result of his conviction that he had been a failure.

Bermuda
Immediately following his father's death, the family moved to Bermuda, where they remained until World War II forced the evacuation of Americans from the island. In Bermuda, Buechner experienced "the blessed relief of coming out of the dark and unmentionable sadness of my father's life and death into fragrance and greenness and light". For a young Buechner, Bermuda became home.

Bermuda left a lasting impression on Buechner. The distinctly British flavor of pre-World War II Bermuda provided in him a lifelong appreciation of English custom and culture, which would later inspire such works as Godric and Brendan. Buechner also frequently mentions Bermuda in his memoirs, including Telling Secrets and The Sacred Journey.

Education and military service
Buechner then attended the Lawrenceville School in Lawrenceville, New Jersey, graduating in 1943. While at Lawrenceville, he met the future Pulitzer Prize winning poet James Merrill; their friendship and rivalry inspired the literary ambitions of both. As Mel Gussow wrote in Merrill's 1995 obituary: "their friendly competition was an impetus for each becoming a writer." Buechner then enrolled at Princeton University. His college career was interrupted by—in Buechner's words—"two years of very undistinguished service" (1944–46) in the Army during World War II, "all of it at several different places in the United States," including a post as "chief of the statistical section in Camp Pickett, Virginia." After the war, he returned to Princeton and graduated with an A.B. in English in 1948 after completing a 77-page senior thesis titled "Notes of the Function of Metaphor in English Poetry." However, as an alumnus, he remained identified as a member of his original Class of 1947. Regarding his time at Princeton, Buechner commented in an interview:

"I really knew two Princetons. The first one was during the war, when everybody was being drafted or enlisting. It was just one drunken farewell party after another. Nobody did any work. I didn't learn anything at all. I was in the Army for two years. When I came back, I was so delighted to be free again that I buckled down and learned a few things."

Literary success and ordination
During his senior year at Princeton University, Buechner received the Irene Glascock Prize for poetry, and he also began working on his first novel and one of his greatest critical successes: A Long Day's Dying, published in 1950. The contrast between the success of his first novel and the commercial failure of his second, The Seasons' Difference (1952), a novel with characters based on Buechner and his adolescent friend James Merrill which developed a more explicit Christian theme, was palpably felt by the young novelist, and it was on this note that Buechner left his teaching position at Lawrenceville to move to New York City and focus on his writing career. In 1952, Buechner began lecturing at New York University and once again received critical acclaim for his short story "The Tiger", published in The New Yorker, which won the O. Henry Award in 1955 {Source needed - the O. Henry Award Wikipedia page lists Jean Stafford as the 1955 winner for her story "In the Zoo"}. Also during this time, he began attending the Madison Avenue Presbyterian Church, where George Buttrick was pastor. It was during one of Buttrick's sermons that Buechner heard the words that inspired his ordination: Buttrick described the inward coronation of Christ as taking place in the hearts of those who believe in him "among confession, and tears, and great laughter." The impact of this phrase on Buechner was so great that he eventually entered the Union Theological Seminary of Columbia University in 1954, on a Rockefeller Brothers Theological Fellowship.

While at Union, Buechner studied under such renowned theologians as Reinhold Niebuhr, Paul Tillich, and James Muilenburg, who helped Buechner in his search for understanding:

"I wanted to learn about Christ – about the Old Testament, which had been his Bible, and the New Testament, which was the Bible about him; about the history of the church, which had been founded on the faith that through him God had not only revealed his innermost nature and his purpose for the world, but had released into the world a fierce power to draw people into that nature and adapt them to that purpose ... No intellectual pursuit had ever aroused in me such intense curiosity, and much more than my intellect was involved, much more than my curiosity aroused. In the unfamiliar setting of a Presbyterian church, of all places, I had been moved to astonished tears which came from so deep inside me that to this day I have never fathomed them, I wanted to learn more about the source of those tears and the object of that astonishment."

Buechner's decision to enter the seminary had come as a great surprise to those who knew him. Even George Buttrick, whose words had so inspired Buechner, observed that, "It would be a shame to lose a good novelist for a mediocre preacher." Nevertheless, Buechner's ministry and writing have ever since served to enhance each other's message.

Following his first year at Union, Buechner decided to take the 1955–56 school year off to continue his writing. In the spring of 1955, shortly before he left Union for the year, Buechner met his wife Judith at a dance given by some family friends. They were married a year later by James Muilenburg in Montclair, N.J., and spent the next four months traveling in Europe. During this year, Buechner also completed his third novel, The Return of Ansel Gibbs.

After his sabbatical, Buechner returned to Union to complete the two further years necessary to receive a Bachelor of Divinity. He was ordained on June 1, 1958, at the same Madison Avenue Presbyterian Church where he had heard George Buttrick preach four years earlier. Buechner was ordained as an evangelist, or minister without pastoral charge. Shortly before graduation, as he considered his future role as minister of a parish, he received a letter from Robert Russell Wicks, formerly the Dean of the Chapel at Princeton, who had since begun serving as school minister at Phillips Exeter Academy. Wicks offered him the job of instituting a new, full-time religion department at Exeter; Buechner decided to take the opportunity to return to teaching and to develop a program that taught religion in depth.

Exeter
In September 1958, the Buechners moved to Exeter. There, Buechner faced the challenge of creating a new religion department and academically rigorous curriculum that would challenge the often cynical views of his new students. "My job, as I saw it, was to defend the Christian faith against its 'cultured despisers,' to use Schleiermacher's phrase. To put it more positively, it was to present the faith as appealingly, honestly, relevantly, and skillfully as I could." During his tenure at Exeter, Buechner taught courses in both the Religion and English departments, and served as school chaplain and minister. Also during this time, the family grew to include three daughters. For the school year 1963–64, the Buechners took a sabbatical on their farm in Rupert, Vermont, during which time Buechner returned to his writing; his fourth book, The Final Beast, was published in 1965. As the first book he had written since his ordination, The Final Beast represented a new style for Buechner, one in which he combined his dual callings as minister and as author.

Buechner recalls of his accomplishments at Exeter: "All told, we were there for nine years with one year's leave of absence tucked in the middle, and by the time we left, the religion department had grown from only one full-time teacher, namely myself, and about twenty students, to four teachers and something in the neighborhood, as I remember, of three hundred students or more." Among these students was the future author John Irving, who included a quotation from Buechner as an epigraph of his book A Prayer for Owen Meany. One of Buechner's biographers, Marjorie Casebier McCoy, describes the effect of his time at Exeter as follows: "Buechner in his sermons had been attempting to reach out to the "cultured despisers of religion." The students and faculty at Phillips Exeter had been, for the most part, just that when he had arrived at the school, and it had been they who compelled him to hone his preaching and literary skills to their utmost in order to get a hearing for Christian faith."

Vermont and last years
In the summer of 1967, after nine years at Exeter and having established the Religion Department, Buechner moved with his family to their farmhouse in Vermont to live year-round. Buechner describes their house in Now and Then:

"Our house is on the eastern slope of Rupert Mountain, just off a country road, still unpaved then, and five miles from the nearest town ... Even at the most unpromising times of year – in mudtime, on bleak, snowless winter days – it is in so many unexpected ways beautiful that even after all this time I have never quite gotten used to it. I have seen other places equally beautiful in my time, but never, anywhere, have I seen one more so."

There Buechner dedicated himself full-time to writing. However, in 1968, Buechner received a letter from Charles Price, the chaplain at Harvard, inviting him to give the Noble Lectures series in the winter of 1969. His predecessors in this role included Richard Niebuhr and George Buttrick, and Buechner was both flattered and daunted by the idea of joining so august a group. When he voiced his concerns, Price replied that he should write "something in the area of 'religion and letters. Thence came the idea to write about the everyday events of life, Buechner writes in Now and Then: "as the alphabet through which God, of his grace, spells out his words, his meaning, to us. So The Alphabet of Grace was the title I hit upon, and what I set out to do was to try to describe a single representative day of my life in a way to suggest what there was of God to hear in it."

Buechner continued to publish occasionally; his last book, A Crazy, Holy Grace: The Healing Power of Pain and Memory, a collection of essays, was released in 2017.

Buechner died on August 15, 2022, at his home in Rupert, Vermont.

Early writing
The publication of A Long Day's Dying catapulted Buechner into early and, in his own words, "undeserved" fame. Of his debut novel, Buechner wrote:

"I took the title from a passage in Paradise Lost where Adam says to Eve that their expulsion from Paradise 'will prove no sudden but a slow pac'd evil,/ A Long Day's Dying to augment our pain,' and with the exception of the old lady Maroo, what all the characters seem to be dying of is loneliness, emptiness, sterility, and such preoccupation with themselves and their own problems that they are unable to communicate with each other about anything that really matters to them very much. I am sure that I chose such a melancholy theme partly because it seemed effective and fashionable, but I have no doubt that, like dreams generally, it also reflected the way I felt about at least some dimension of my own life and the lives of those around me."

Conductor and composer Leonard Bernstein commented on the novel:

"I have rarely been so moved by a perception. Mr. Buechner shows a remarkable insight into one of the least easily expressible tragedies of modern man; the basic incapacity of persons really to communicate with one another. That he has made this frustration manifest, in such a personal and magnetic way, and at the age of twenty-three, constitutes a literary triumph."

A Long Day's Dying continues to be one of Buechner's most successful works, both critically and commercially (it was reissued in 2003). However, his second novel, The Season's Difference, published in 1952, in Buechner's words, "fared as badly as the first one had fared well."

The publication of Buechner's third novel, The Return of Ansel Gibbs (written while on sabbatical from Union Theological Seminary) coincided with Buechner's ordination and move to Exeter, where he began to publish non-fiction.

Nonfiction and memoirs
Buechner's works of non-fiction, which cover several sub-genres including sermons, daily reflections, and memoirs, altogether outnumber his works of fiction. His first such work, The Magnificent Defeat, is a collection of sermons, signifying his growth into his career as a minister at Exeter. Throughout his career, he published several more volumes of sermons, most recently Secrets in the Dark: a life in sermons, which includes a "more or less [chronological] culling" of his sermons, "together with the most recent and hitherto unpublished ones."

To date, Buechner's corpus of memoir includes four volumes: The Sacred Journey (1982), Now and Then (1983), Telling Secrets (1991), and The Eyes of the Heart (1999). Of all his books, The Sacred Journey and Telling Secrets consistently rank among his bestselling. Of his interest in memoir, Buechner wrote in the introduction to The Sacred Journey:

"About ten years ago I gave a set of lectures at Harvard in which I made the observation that all theology, like all fiction, is at its heart autobiography, and that what a theologian is doing essentially is examining as honestly as he can the rough-and-tumble of his own experience with all its ups and downs, its mysteries and loose ends, and expressing in logical, abstract terms the truths about human life and about God that he believes he has found implicit there. More as a novelist than as a theologian, more concretely than abstractly, I determined to try to describe my own life as evocatively and candidly as I could in the hope that such glimmers of theological truth as I believed I had glimpsed in it would shine through my description more or less on their own. It seemed to me then, and seems to me still, that if God speaks to us at all in this world, if God speaks anywhere, it is into our personal lives that he speaks."

Buechner's most recent publications include Buechner 101: Essays and Sermons by Frederick Buechner (2014), The Remarkable Ordinary: How to Stop, Look, and Listen to Life (2017), and A Crazy, Holy Grace: The Healing Power of Pain and Memory (2017).

Later novels: The Book of Bebb, Godric, Brendan
Concurrent with Buechner's delivery of the Noble Lectures, he developed the most significant character of his later career, Leo Bebb.

The Book of Bebb tetralogy proved to be one of Buechner's most well-known works. Published in the years from 1972 to 1977, it brought Buechner to a much wider audience, and gained him very positive reviews (Lion Country, the first book in the series, was a finalist for the National Book Award in 1971). Of writing the series, Buechner says: "I had never known a man like Leo Bebb and was in most ways quite unlike him myself, but despite that, there was very little I had to do by way of consciously, purposefully inventing him. He came, unexpected and unbidden, from a part of myself no less mysterious and inaccessible than the part where dreams come from; and little by little there came with him a whole world of people and places that was as heretofore unknown to me as Bebb was himself." In this series, Buechner experimented for the first time with first-person narrative, and discovered that this, too, opened new doors. His next work, Godric, published in 1980, was nominated for the Pulitzer Prize. The novel, a historical fiction, is written in the first person from the perspective of Saint Godric of Finchale, a 12th-century English hermit.

Brendan (1987), a work of historical fiction like Godric, draws from the life of the 6th-century Irish monk Saint Brendan the Navigator. Experimenting further with the narrative technique Buechner employed to such dramatic effect in Godric, Brendan interweaves history and legend in an evocative portrayal of the sixth-century Irish saint as seen through the eyes of Finn, his childhood friend and loyal follower. Buechner's colorful recreation of the Celtic world of fifteen hundred years ago earned him the Christianity and Literature Belles Lettres Prize in 1987.

Tributes and legacy
In 2001, Californian rock band Daniel Amos released a double album titled Mr. Buechner's Dream. The album contains over thirty songs and pays tribute to Frederick Buechner, "who has been a major inspiration on the band's lyrics for years."

In the words of The Reverend Samuel Lloyd, former dean of Washington National Cathedral, Buechner's words "have nurtured the lives of untold seekers and followers" through "his capacity to see into the heart of every day":

"Buechner's theological efforts are never systematic treatises but instead short, highly literary productions in most of which he draws explicit links with fiction-writing generally and his own fiction in particular...Buechner's 1969 Noble Lectures at Harvard, published in 1970 as The Alphabet of Grace, comprise a slender volume which is one of his most important and revealing works. Here the intimate relationship Buechner sees among fiction, theology, and autobiography is first made clear and fully embodied; and the book itself is a thoroughly lyrical piece."

Buechner's combination of literary style with approachable subject matter has affected contemporary Christian literature: "In my view," writes his biographer Marjorie McCoy, "Buechner is doing a distinctively new thing on the literary scene, writing novels that are theologically exciting without becoming propaganda, and doing theology with artistic style and imagination." Buechner's earliest works, written before his entrance into Union Theological Seminary, were hailed as profoundly literary works, notable for their dense, descriptive style. Of his first novel, A Long Day's Dying, David Daiches wrote: "There is a quality of civilized perception here, a sensitive and plastic handling of English prose and an ability to penetrate to the evanescent core of a human situation, all proclaiming major talent." From this promising beginning, however, it has been the application of Buechner's literary talent to theological issues that has continued to fascinate his audience:

"Frederick Buechner has been one of our most interesting and least predictable writers. Others might have repeated their success or failures, but he has not. From the sophisticated urban world of that first book, through The Return of Ansel Gibbs with its world of politics and public affairs, to the private, half-haunted pastoral world of The Entrance to Porlock, he has created a series of novels of startlingly different moods and manners, people and places. The one constant has been the masterful use of great stylistic powers to organize and control his highly original and complex vision of life."

Of his more recent style, the pastor and author Brian D. McLaren says:

"I have no desire to analyze what makes Buechner's writing and preaching so extraordinary. Neither do I want to account for Bob Dylan's raspy mystique, the peculiar beauty of a rainbow trout in a riffle, or a thunderstorm's magnetic terror. I simply want to enjoy them. They all knock me out of analysis and smack me clear into pleasure and awe."

Throughout Buechner's work his hallmark as a theologian and autobiographer is his regard for the appearance of the divine in daily life. By examining the day-to-day workings of his own life, Buechner seeks to find God's hand at work, thus leading his audience by example to similar introspection. The Reverend Samuel Lloyd describes his "capacity to see into the heart of every day," an ability that reflects the significance of daily events onto the reader's life as well. In the words of the preacher Barbara Brown Taylor: "From [Buechner] I've learned that the only limit to the revelation going on all around me is my willingness to turn aside and look."

Buechner Writer's Workshop at Princeton
Princeton Theological Seminary hosts an annual Buechner Writing Workshop. The workshop is designed to "encourage, educate, and inspire writers to communicate their Christian faith with clarity and power in the tradition of Frederick Buechner". Past speakers have included authors such as Barbara Brown Taylor, Rachel Held Evans, Philip Gulley, M. Craig Barnes, Philip Yancey, and Kathleen Norris..

Buechner Institute at King University
Inaugurated in 2008 at King University, the former King College, the Buechner Institute was dedicated to the work and example of Buechner, exploring the intersections and collisions of faith and culture that define our times.

Dale Brown, the founding director of the Buechner Institute, was the author of numerous articles and the recent critical biography, The Book of Buechner: A Journey Through His Writings.

The Buechner Institute sponsored weekly convocations in Memorial Chapel on the campus of King University that featured speakers from a variety of backgrounds who examined the ways in which faith informs art and public life and cultivate conversation about what faith has to do with books, politics, social discourse, music, visual arts, and more.

Additionally, the Buechner Institute sponsored the Annual Buechner Lecture. The following is the list of lecturers invited to speak thus far:
 * 2008: Frederick Buechner (inaugural lecture)
 * 2009: Barbara Brown Taylor
 * 2010: Ron Hansen
 * 2011: Katherine Paterson
 * 2012: Marilynne Robinson
 * 2013: Kathleen Norris (poet)
 * 2013: Doug Worgul

A summer symposium on the work of Frederick Buechner, Buechnerfest, was featured in 2010 and 2012. Attendees from around the country spent a week of reading and entertainment on the Virginia/Tennessee border.

The work of the institute was guided by a local governing board and a national advisory board. National board members included Doris Betts, Walter Brueggemann, Scott Cairns, Michael Card, Elizabeth Dewberry, Tim Gautreaux, Philip Gulley, Ron Hansen, Roy Herron, Silas House, Richard Hughes, Thomas G. Long, Tom Lynch, Brian McLaren, Carrie Newcomer, Kathleen Norris, Katherine Paterson, Eugene H. Peterson, Charles Pollard, Barbara Brown Taylor, Will Willimon, John Wilson, Philip Yancey, Doug Worgul, and others.

In 2015, after the death of Dr. Dale Brown, founding director, and at the request of the Buechner Literary Assets, LLC, the Buechner Institute became the King Institute for Faith and Culture. The King Institute for Faith and Culture is a continuation of conversations between faith, art, and culture started by the Buechner Institute.

In the media
Buechner's work has been praised highly by many reviewers of books, with the distinct exception of his second novel, The Season's Difference, which was universally panned by critics and remains his biggest commercial flop. His later novels, including the Book of Bebb series and Godric, received praise; in his 1980 review of Godric, Benjamin DeMott summed up a host of positive reviews, saying "All on his own, Mr. Buechner has managed to reinvent projects of self-purification and of faith as piquant matter for contemporary fiction, producing in a single decade a quintet of books each of which is individual in concerns and knowledge, and notable for literary finish." In 1982, author Reynolds Price greeted Buechner's The Sacred Journey as "a rich new vein for Buechner – a kind of detective autobiography" and "[t]he result is a short but fascinating and, in its own terms, beautifully successful experiment."

Buechner has occasionally been accused of being too "preachy;" a 1984 review by Anna Shapiro in the New York Times notes "But for all the colloquialism, there is something, well, preachy and a little unctuous about making yourself an exemplar of faith. Insights that would do for a paragraph are dragged out with a doggedness that will presumably bring the idea home to even the most resistant and inattentive." The sentiments expressed by Cecelia Holland's 1987 Washington Post review of Buechner's novel, Brendan, are far more common. She writes,"In our own time, when religion is debased, an electronic game show, an insult to the thirsty soul, Buechner's novel proves again the power of faith, to lift us up, to hold us straight, to send us on again."

In 2008 Rich Barlowe wrote of Buechner in The Boston Globe, "Who knows? The words are Frederick Buechner's mantra. Over the course of an hourlong chat with the writer and Presbyterian minister in his kitchen, they recur any number of times in response to questions about his faith and theology. Dogmatic religious believers would dismiss the two words as the warning shot of doubt. But for Buechner, it is precisely our doubts and struggles that mark us as human. And that insight girds his theological twist on Socrates: The unexamined human life is a lost chance to behold the divine." In 2002, Richard Kauffman interviewed Buechner for The Christian Century upon the publication of Speak What We Feel (Not What We Ought to Say). Buechner answered the question "Do you envision a particular audience when you write?" by saying "I always hope to reach people who don't want to touch religion with a ten-foot pole. The cultured despisers of religion, Schleiermacher called them. Maybe some of my books reach them. But most of my readers, as far as I can tell, aren't that type. Many of them are ministers. They say, 'You've given us something back we lost and opened up doors we didn't think could be opened for people.'"

Selected bibliography

 * A Long Day's Dying, 1950 (ISBN 978-0972429542)
 * The Magnificent Defeat, 1966 (ISBN 9780060611743)
 * Telling the Truth: the Gospel as tragedy, comedy, and fairy tale, 1977 (ISBN 9780060611569)
 * The Book of Bebb, 1979 (ISBN 9780062517692)
 * Godric, 1980 (ISBN 9780060611620)
 * The Sacred Journey, 1982 (ISBN 9780060611835)
 * Brendan, 1987 (ISBN 9780060611781)
 * Telling Secrets, a Memoir, 1991 (ISBN 9780060611811)
 * Listening to Your Life: Daily Meditations with Frederick Buechner, 1992 (ISBN 9780060698645)
 * Secrets in the Dark: A Life in Sermons, 2006 (ISBN 978-0-06-084248-2)

title: Frederick Buechner


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Talk:Sharkovskii's theorem

Proof
Can someone point me to an accessible version of the proof of this theorem ? I have tried looking on arxiv etc. to add it to the page, but have been unlucky so far. AmarChandra 17:00 May 23, 2004 (UTC)

stable cycles appear in Sarkovskii order in the bifurcation diagram, starting with 1 and ending with 3, as the parameter is varied. - I doubt that this is true. Isn't there bifurcation after 3, leading to stable cycles of period 6 for slightly larger parameters?

Also, Sarkovskii's theorem doesn't say anything about the way the period of stable cycles change as the parameter changes, so I think this statement, even if true, confuses the matter. AxelBoldt 01:46 Sep 30, 2002 (UTC)

There are stable cycles of various orders, including 5 as well as 6, 12, ..., after the 3-cycle. What counts is the first time the cycle appears. -phma

 * Oh, ok, I'll put the statement back then. AxelBoldt 21:26 Dec 22, 2002 (UTC)

Spelling
We should move this term Sarkovskii's theorem to proper term Sharkovsky's theorem, since it is named after Ukrainian mathematician Oleksandr Mikolaiovich Sharkovsky and hence goes the English spelling. Best regards. --XJam 12:27 Dec 17, 2002 (UTC)

Google gives about three times as many hits for Sarkovskii's theorem than for Sharkovsky's theorem, so I suggest we leave the article at the more common spelling. AxelBoldt 21:26 Dec 22, 2002 (UTC)
 * I disagree in full. Bad habit. Don't mind the Google. Thousand times spoken lie becomes a truth. If Google is wrong, why should be Wikipedia then too. And still, if we translate his first name in English, we should write Olexandr and, I guess, not Oleksandr. But as it seems, nobody cares that. Nevertheless we should be even more precise here. That is my strong opinion. --XJam 23:32 Dec 23, 2002 (UTC)

 * Why do you think that Sarkovskii is wrong and Sharkovsky is right? AxelBoldt 02:49 Dec 24, 2002 (UTC)
 * I believe the spelling Sarkovskii comes from other languages than English, probably mostly from French and German language. Have you checked searching Sharkovsky just in Google's English pages? I haven't. But I guess it would give more terms than Sarkovskii. In Slavic languages a letter "s" is completely different from a letter "sh". I tried to find a person, who is responsible for this theorem under Sarkovskii, but I failed. It was just my lucky guess that I really found him. But I might be wrong after all too. I am just trying to be accurate as posible as I can. Someone is more careful regarding strictly math terms and someone regarding related math terms as names, surnames, birthplaces and such are. --XJamRastafire 10:36 Dec 24, 2002 (UTC)

 * Actually, I've seen Šharkovksii for the Ukrainian spelling. I agree that the best English spelling is probably Sharkovsky.  Also, I have seen some experienced Wikipedians argue that articles about theorems should be named X theorem rather than X's theorem, although I am not sure I agree.  One thing seems clear: whatever the name of the article, someone should ensure that there are suitable redirects from the other candidates. ---CH 21:02, 13 May 2006 (UTC)

On both his personal web page and his page at the Ukrainian Academic of Sciences he spells it Sharkovsky. A survey of my collection of textbooks on dynamical systems---all in English---reveals that Charkovsky, Sharkovskii, Sharkovsky, and Sarkovskii are all in use. But since Sharkovsky spells it Sharkovsky, it seems like Sharkovsky is the way to go. Dave Feldman (talk) 00:00, 14 July 2011 (UTC)

 * I was just thinking about this. While I was at university, I was taught that the name is known by different spellings, similarly to Chebyshev, apparently as a result of different transliterations from the Cyrillic.
 * IIRC, the worksheet on which I was taught about his theorem had it as Šarkovskii (except where explicitly listing the different spellings). But I don't remember now what other spellings it listed.  On the English WP I see Sharkovsky and Sharkovskii.  The only other form I see in the sources is Sarkovskii.  But I see a few others in other language Wikipedias – Charkovski, Scharkowskyj, Szarkowski, Szarkowskiego.  That said, the last of these appears to be a possessive or genitive form.  If I put the Cyrillic into Google Translate, it's a bit weird: Олекса́ндр Миколайович Шарко́вський becomes Oleksandr Mykolayovych Sharkovskyi, but Шарко́вський by itself becomes Sharkovsky.
 * Are you sure about Šharkovksii? This seems erroneous - I would expect 'Š' to already make a /ʃ/ sound, rendering the 'h' spurious.
 * It would be good if we could find something about the different spellings to write on WP, probably on the Oleksandr Mykolayovych Sharkovsky page rather than here. — Smjg (talk) 01:19, 12 September 2022 (UTC)

Clarification needs clarity
The article says:

"3, 5, 7, 9, ... ,2·3, 2·5, 2·7, ..., 2^2·3, 2^2·5, ..... , 2^4, 2^3, 2^2, 2, 1.

We start, that is, with the odd numbers in increasing order, then 2 times the odds, 4 times the odds, etc.,. . ."

The problem with this "clarification" is that many people unfamiliar with Sharkovskii's Theorem will wonder if this "etc." continues with 6 times the odds or with 8 times the odds -- something the "clarification" doesn't clarify.Daqu (talk) 03:00, 18 March 2008 (UTC)

Article name consensus?
Was there ever consensus on the title of this article? Personally, I'd prefer Sarkovskii, but I'm not going to get into that. The preferred name is debatable, but that the spelling should be consistent throughout the article is not, so I've changed all "Sarkovskii"s to "Sharkovskii"s since that is the current page title. Tcnuk (talk) 13:11, 2 March 2010 (UTC)

 * As the mathematician's name is Александр Николаевич Шарковский, I see little room to prefer the spelling Sarkovskii.--Hagman (talk) 14:45, 26 November 2016 (UTC)

Burns/Hasselblatt paper
I added a link to a draft paper by Burns and Hasselblatt about the theorem. I put it in as an extlink rather than a reference since I don't know if it has been formally published. An earlier version was submitted in 2007. Both links are from Richard Lipton's recent blog post relating the theorem (and some other topics) to computational complexity. 71.141.88.54 (talk) 22:40, 27 February 2011 (UTC)

Well-ordering - relevant?
The recently-added sentence: Note that this ordering is not a well-ordering, since the set $$\{2^k \ \mid\ k \in \mathbb{N}\}$$ doesn't have a least element seems to be true, but I can't see any relevance the article - should it be deleted? --catslash (talk) 23:45, 30 December 2012 (UTC)

 * I think in a well-order you can 'only go to infinity once', so there wouldn't be much significance to the fact a function has only finitely many periodic orbits. Otherwise, all functions with infinitely many periods would have every period. Gred Sixteen (talk) 13:14, 25 August 2014 (UTC)

 * Pretty sure that $$\{2^k \ \mid\ k \in \mathbb{N}\}$$ has a least element. — Preceding unsigned comment added by 139.67.20.29 (talk) 9 September 2014 (UTC)

 * $$\{2^k \ \mid\ k \in \mathbb{N}\}$$ has a least element under the usual natural number order, but under the Sharkovskii order it doesn't, since Sharkovskii orders ... < 8 < 4 < 2 < 1. Which is the content of the wiki remark I guess. Jan Burse (talk) 21:20, 20 November 2016 (UTC)

The misleading note has been removed by on 12 September 2015 in Special:Diff/680708792, then the topic was expanded and explained by  on 13 February 2019 in Special:Diff/883119856. --CiaPan (talk) 09:18, 24 July 2019 (UTC)

Bad counterexample
The function $$f(x)=(1-x)^{-1}$$ is named as a counterexample showing that continuity is needed. However, to me it seems more importantly a counterexample that shows that the $$I$$ in $$f\colon I\to I$$ must be an interval, i.e., a connected subset of the reals. After all, $$f(x)=(1-x)^{-1}$$ is a continuous map $$f\colon I\to I$$ if one allows $$I=\mathbb R\setminus\{0,1\}$$ (as well as if one allows $$I=\mathbb R\cup \{\infty\}$$). That dropping continuity allows arbitrary behaviour is clear anyway.--Hagman (talk) 14:39, 26 November 2016 (UTC)

 * I have fixed and extended the counter-example in Special:Diff/882409296. Hope it is both redable and correct now. :) --CiaPan (talk) 13:38, 10 February 2019 (UTC)

Sequence
Is Sharkovski order an integer sequence ? --Adam majewski (talk) 13:48, 11 November 2021 (UTC)
 * Nope. It's not an integer sequence because it is not even a sequence. --CiaPan (talk) 20:51, 11 November 2021 (UTC)
 * A GRAPH THEORETIC PROOF OF SHARKOVSKY'S THEOREM ON THE PERIODIC POINTS OF CONTINUOUS FUNCTIONS by CHUNG-WU HO AND CHARLES MORRIS : "Sharkovsky's theorem says that a function f:R—>R having a point of period m, must also have points of period n precisely when m precedes n in the above sequence." So it calls it a sequence = an an ordered list of integers. --Adam majewski (talk) 15:19, 14 November 2021 (UTC)
 * That's wrong. A sequence is commonly defined (→Sequence) as a function on all natural numbers (infinite sequences) or some initial segment $$1, 2, \ldots n$$ of them (finite sequences). Sharkovskii's theorem defines an order in a set of all natural numbers, which is infinite. An infinite sequence has no last element, because natural numbers (a set of indices) have no last element. However, the ordering has a last element, namely 1. As such it's not a sequence. Q.E.D. --CiaPan (talk) 18:27, 14 November 2021 (UTC) Edited. --CiaPan (talk) 21:20, 14 November 2021 (UTC)

 * , here is another approach. Consider the first row of the Sharkovskii's ordering description. It enumerates all odd natural numbers (except 1):
 * $$3 \quad 5 \quad 7 \quad 9 \quad 11 \ \ldots \ (2n+1)\cdot2^{0} \ \ldots$$
 * Odd numbers make an infinite sequence, thus exhausting all natural numbers as a set of indices. Anyway, then another infinite sequence goes, appended after the first one – those are all $$(2n+1)\cdot 2.$$ And then, all $$(2n+1)\cdot 2^2.$$ And an infinite sequence of infinite sequences of even numbers follows. Plus the terminating $$1$$ at the end (!).
 * The above construction makes it impossible to define a position (index) of any even term, as there is an infinite set of numbers preceding it (all odd numbers, at least). This contradicts a definition of a sequence as a function, that is an assignment of values (terms) to arguments (indices from a set of natural numbers). --CiaPan (talk) 10:02, 7 December 2021 (UTC)
 * Right. Thx. --Adam majewski (talk) 16:09, 8 December 2021 (UTC)

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

title: Talk:Sharkovskii's theorem


text:
Audubon County, Iowa

Audubon County is a county in the U.S. state of Iowa. As of the 2020 census, the population was 5,674, making it Iowa's third-least populous county. Its county seat is Audubon. The county was named after John James Audubon, the naturalist and artist.

History
Audubon County was formed on January 15, 1851, from sections of Pottawattamie County. It was named after John James Audubon. The current Audubon County Court House was opened in 1940.

Geography
According to the U.S. Census Bureau, the county has an area of 443 sqmi, of which 443 sqmi is land and 0.4 sqmi (0.1%) is water.

Major highways

 * US 71.svg U.S. Highway 71
 * Elongated circle 44.svg Iowa Highway 44
 * Elongated circle 173.svg Iowa Highway 173

Adjacent counties

 * Carroll County (north)
 * Guthrie County (east)
 * Cass County (south)
 * Shelby County (west)

2020 census
The 2020 census recorded a population of 5,674 in the county, with a population density of. 97.41% of the population reported being of one race. 94.87% were non-Hispanic White, 0.30% were Black, 1.52% were Hispanic, 0.09% were Native American, 0.09% were Asian, 0.02% were Native Hawaiian or Pacific Islander and 3.12% were some other race or more than one race. There were 2,787 housing units of which 2,498 were occupied.

2010 census
The 2010 census recorded a population of 6,119 in the county, with a population density of. There were 2,972 housing units, of which 2,617 were occupied.

2000 census
As of the census of 2000, there were 6,830 people, 2,773 households, and 1,927 families residing in the county. The population density was 15 /mi2. There were 2,995 housing units at an average density of 7 /mi2. The racial makeup of the county was 99.17% White, 0.15% Black or African American, 0.09% Native American, 0.19% Asian, 0.03% from other races, and 0.38% from two or more races. 0.48% of the population were Hispanic or Latino of any race.

There were 2,773 households, out of which 30.10% had children under the age of 18 living with them, 61.40% were married couples living together, 5.60% had a female householder with no husband present, and 30.50% were non-families. 28.20% of all households were made up of individuals, and 16.70% had someone living alone who was 65 years of age or older. The average household size was 2.40 and the average family size was 2.94.

In the county, the population was spread out, with 25.90% under the age of 18, 5.00% from 18 to 24, 22.70% from 25 to 44, 22.90% from 45 to 64, and 23.50% who were 65 years of age or older. The median age was 42 years. For every 100 females there were 92.00 males. For every 100 females age 18 and over, there were 89.10 males.

The median income for a household in the county was $32,215, and the median income for a family was $37,288. Males had a median income of $28,090 versus $17,528 for females. The per capita income for the county was $17,489. About 6.70% of families and 7.70% of the population were below the poverty line, including 8.20% of those under age 18 and 7.80% of those age 65 or over.

Cities

 * Audubon
 * Brayton
 * Exira
 * Gray
 * Kimballton

Townships
Audubon County is divided into twelve townships:

 * Audubon
 * Cameron
 * Douglas
 * Exira
 * Greeley
 * Hamlin
 * Leroy
 * Lincoln
 * Melville
 * Oakfield
 * Sharon
 * Viola

Population ranking
The population ranking of the following table is based on the 2020 census of Audubon County. † county seat

title: Audubon County, Iowa


text:
Appanoose County, Iowa

Appanoose County is a county in the U.S. state of Iowa. As of the 2020 census, the population was 12,317. Its county seat is Centerville.

History
Appanoose County was formed on February 17, 1843, from open territory. It was named for the Meskwaki Chief Appanoose, who did not engage in war against Black Hawk, advocating peace. The present county seat was formerly called Chaldea, and was later renamed to Senterville in honor of Congressman William Tandy Senter of Tennessee. In April 1848, the courthouse, constructed at the expense of $160, was put into use and served as such until 1857. The second courthouse was opened in 1864, and was burned down to the first floor during an explosive Fourth of July fireworks demonstration. The third courthouse was dedicated on May 21, 1903, and remains in use.

In the summer of 1832 a company of cavalry set out from Davenport on a reconnaissance which extended as far west as Fort Leavenworth. They passed through what would become Appanoose County in a nearly southwest direction, passing near the present city of Moulton, camping overnight at a spring southwest of Cincinnati, and leaving the area and crossing into Missouri near the southwest corner of Pleasant Township. Early settlers in search of claims found two trails. The route taken by the cavalrymen and another with a general north–south direction, passing through Washington Township, and known as the bee trace and used in the summer by honey collectors. A post office in Washington Township was called Beetrace. The Beetrace post office was discontinued on March 1, 1886. This may have been originally an Indian trail. The first settlers say that it was a tolerably well-defined wagon road as far north as the Beetrace post office and that it could be followed easily into Taylor Township. Another "bee-trace" ran from Missouri diagonally through Davis County and terminated near Unionville.

Geography
According to the U.S. Census Bureau, the county has a total area of 516 sqmi, of which 497 sqmi is land and 19 sqmi (3.7%) is water. Rathbun Reservoir, created by damming the Chariton River, is its main physical feature.

Major highways

 * Circle sign 2.svg Iowa Highway 2
 * Circle sign 5.svg Iowa Highway 5
 * Elongated circle 202.svg Iowa Highway 202

Adjacent counties

 * Monroe County (north)
 * Wapello County (northeast)
 * Lucas County (northwest)
 * Davis County (east)
 * Schuyler County, Missouri (southeast)
 * Putnam County, Missouri (southwest)
 * Wayne County (west)

2020 census
The 2020 census recorded a population of 12,317 in the county, with a population density of. 96.66% of the population reported being of one race. 93.03% were non-Hispanic White, 0.61% were Black, 1.88% were Hispanic, 0.19% were Native American, 0.57% were Asian, 0.06% were Native Hawaiian or Pacific Islander and 3.66% were some other race or more than one race. There were 6,306 housing units of which 5,320 were occupied.

2010 census
The 2010 census recorded a population of 12,884 in the county, with a population density of. There were 6,633 housing units, of which 5,627 were occupied.

2000 census
At the 2000 census there were 13,721 people, 5,779 households, and 3,802 families in the county. The population density was 28 /mi2. There were 6,697 housing units at an average density of 14 /mi2. The racial makeup of the county was 98.16% White, 0.42% Black or African American, 0.17% Native American, 0.26% Asian, 0.01% Pacific Islander, 0.27% from other races, and 0.71% from two or more races. 0.98%. were Hispanic or Latino of any race.

Of the 5,779 households 28.40% had children under the age of 18 living with them, 53.10% were married couples living together, 8.80% had a female householder with no husband present, and 34.20% were non-families. 29.90% of households were one person and 15.40% were one person aged 65 or older. The average household size was 2.34 and the average family size was 2.89.

23.70% of the people are under the age of 18, 7.80% from 18 to 24, 25.10% from 25 to 44, 23.50% from 45 to 64, and 20.00% 65 or older. The median age was 41 years. For every 100 females there were 91.50 males. For every 100 females age 18 and over, there were 89.50 males.

The median household income was $28,612 and the median family income was $35,980. Males had a median income of $27,449 versus $20,452 for females. The per capita income for the county was $14,644. About 10.10% of families and 14.50% of the population were below the poverty line, including 16.00% of those under age 18 and 14.10% of those age 65 or over.

Cities

 * Centerville
 * Cincinnati
 * Exline
 * Moravia
 * Moulton
 * Mystic
 * Numa
 * Plano
 * Rathbun
 * Udell
 * Unionville

Townships
Appanoose County is divided into seventeen townships:

 * Bellair
 * Caldwell
 * Chariton
 * Douglas
 * Franklin
 * Independence
 * Johns
 * Lincoln
 * Pleasant
 * Sharon
 * Taylor
 * Udell
 * Union
 * Vermillion
 * Walnut
 * Washington
 * Wells

Population ranking
The population ranking of the following table is based on the 2020 census of Appanoose County.

† county seat

title: Appanoose County, Iowa


text:
Allamakee County, Iowa

Allamakee County is the northeasternmost county in the U.S. state of Iowa. As of the 2020 census, the population was 14,061. Its county seat is Waukon.

History
Allamakee County was formed on February 20, 1847. The derivation of the name is debated, some believing it was the name of an Indian chief, others think it was named for Allen Magee, an early historic trader. The first Allamakee County Courthouse in Waukon, built in 1861, now serves as the Allamakee County Historical Museum. The present Allamakee County Court House was built in 1940. Both courthouse buildings are listed on the National Register of Historic Places.

Geography
According to the U.S. Census Bureau, the county has a total area of 659 sqmi, of which 639 sqmi is land and 20 sqmi (3.0%) is water.

In the northern part of the county is the Upper Iowa River. In the southern part is the Yellow River. The eastern boundary is the Mississippi River. All offer scenic and recreational opportunities, particularly in Yellow River State Forest.

French Creek flows north of Waukon, outside the city limits. Paint Creek, named after Paint Rock Bluff, flows out of the south of Waukon. Norfolk creek originates in the western outskirts of Waukon and is effluent to the Yellow River. Clear Creek flows into Lansing. Village Creek flows through essentially rural terrain. All are tributary to the Mississippi River.

The landforms encountered in the county are very unlike those found in most of Iowa, which is mostly absent Glacial Drift. As part of the Driftless Area, the county was ice free during the last ice age, and as one progresses to the Mississippi River, the streams and rivers display high-walled canyons carved of Silurian period bedrock. This Driftless Area also includes parts of Clayton, Fayette, Winneshiek, Howard, Dubuque, and Jackson Counties.

Major highways

 * US 18.svg U.S. Highway 18
 * US 52.svg U.S. Highway 52
 * Circle sign 9.svg Iowa Highway 9
 * Elongated circle 26.svg Iowa Highway 26
 * Elongated circle 51.svg Iowa Highway 51
 * Elongated circle 76.svg Iowa Highway 76

Adjacent counties

 * Houston County, Minnesota (north)
 * Vernon County, Wisconsin (northeast)
 * Crawford County, Wisconsin (east)
 * Clayton County (south)
 * Winneshiek County (west)
 * Fayette County (southwest)

2020 census
The 2020 census recorded a population of 14,061 in the county, with a population density of. 96.88% of the population reported being of one race. 81.08% were non-Hispanic White, 1.10% were Black, 8.68% were Hispanic, 0.65% were Native American, 0.29% were Asian, 0.04% were Native Hawaiian or Pacific Islander and 8.17% were some other race or more than one race. There were 7,668 housing units of which 5,797 were occupied.

2010 census
The 2010 census recorded a population of 14,330 in the county, with a population density of. There were 7,617 housing units, of which 5,845 were occupied.

2000 census
As of the census of 2000, there were 14,675 people, 5,722 households, and 3,931 families residing in the county. The population density was 23 /mi2. There were 7,142 housing units at an average density of 11 /mi2. The racial makeup of the county was 95.88% White, 0.14% Black or African American, 0.18% Native American, 0.27% Asian, 0.01% Pacific Islander, 2.82% from other races, and 0.70% from two or more races. 3.54% of the population were Hispanic or Latino of any race.

There were 5,722 households, out of which 30.60% had children under the age of 18 living with them, 58.40% were married couples living together, 6.60% had a female householder with no husband present, and 31.30% were non-families. 27.50% of all households were made up of individuals, and 14.30% had someone living alone who was 65 years of age or older. The average household size was 2.49 and the average family size was 3.02.

In the county, the population was spread out, with 25.40% under the age of 18, 7.00% from 18 to 24, 25.60% from 25 to 44, 23.60% from 45 to 64, and 18.40% who were 65 years of age or older. The median age was 40 years. For every 100 females there were 100.20 males. For every 100 females age 18 and over, there were 98.90 males.

The median income for a household in the county was $33,967, and the median income for a family was $40,589. Males had a median income of $26,122 versus $19,098 for females. The per capita income for the county was $16,599. About 6.40% of families and 9.60% of the population were below the poverty line, including 11.80% of those under age 18 and 8.10% of those age 65 or over.

Notable sites

 * Effigy Mounds National Monument is found in the southeast corner of the county.
 * Upper Mississippi River National Wildlife and Fish Refuge encompasses the River.
 * Driftless Area National Wildlife Refuge, a collection of small, non-contiguous parcels harboring two endangered species.
 * Yellow River State Forest is a four-season state park.

Media

 * The Waukon Standard
 * The Postville Herald-Leader

Cities

 * Harpers Ferry
 * Lansing
 * New Albin
 * Postville (part)
 * Waterville
 * Waukon

Townships
Allamakee County is divided into eighteen townships:

 * Center
 * Fairview
 * Franklin
 * French Creek
 * Hanover
 * Iowa
 * Jefferson
 * Lafayette
 * Lansing
 * Linton
 * Ludlow
 * Makee
 * Paint Creek
 * Post
 * Taylor
 * Union City
 * Union Prairie
 * Waterloo

Unincorporated communities

 * Church
 * Dorchester
 * Ludlow
 * Lycurgus
 * Rossville
 * Volney

Ghost towns

 * Columbus
 * Hardin
 * Ion
 * Myron
 * Village Creek

Population ranking
The population ranking of the following table is based on the 2020 census of Allamakee County.

† county seat

title: Allamakee County, Iowa


text:
William Smith

William, Willie, Will, Bill, or Billy Smith may refer to:

Academics

 * William Smith (Master of Clare College, Cambridge) (1556–1615), English academic
 * William Smith (antiquary) (c. 1653–1735), English antiquary and historian of University College, Oxford
 * William Smith (scholar) (1711–1787), English classical scholar and Anglican Dean of Chester
 * William Smith (Episcopal priest) (1727–1803), Scottish-born first provost of University of Pennsylvania
 * William Pitt Smith (1760–1796), American physician, educator and theological writer
 * William Andrew Smith (1802–1870), American college president and clergyman
 * William Smith (lexicographer) (1813–1893), English editor and publisher of dictionaries
 * William Robertson Smith (1846–1894), Scottish philologist, physicist, archaeologist and Biblical critic
 * William Benjamin Smith (1850–1934), American professor of mathematics at Tulane University
 * William Ramsay Smith (1859–1937), Australian anthropologist
 * William George Smith (1866–1918), Scottish psychologist
 * William Hall Smith (1866–after 1920), President of Mississippi Agricultural and Mechanical College, 1916–1920
 * William Cunningham Smith (1871–1943), American academic of English literature, university administrator and writer
 * William Roy Smith (1876–1938), American academic historian
 * William Charles Smith (1881–1972), English musicologist
 * William Newton-Smith (1943–2023), Anglo-Canadian philosopher of science

Arts and entertainment

 * William "Gentleman" Smith (1730–1819), English stage star
 * William Henry Smith (1806–1872), American author of 1844 temperance play The Drunkard
 * William Smith (actor) (1933–2021), American character performer
 * William Smith (17th-century actor) (died 1696), British actor
 * William Smith (teacher) (born 1939), South African television science and mathematics presenter
 * Will Smith (comedian) (born 1971), English actor and writer

Art and literature

 * William Smith (poet) (before 1570–after 1606), English sonneteer
 * William Thompson Russell Smith (1812–1896), Scottish-American painter
 * William Collingwood Smith (1815–1887), English painter
 * William Jardine Smith (1834–1884), Australian writer and editor
 * William Brooke Smith (before 1880–1908), American artist
 * William Twigg-Smith (1883–1950), New Zealand artist
 * William Hart-Smith (1911–1990), New Zealand/Australian poet
 * William E. Smith (artist) (1913–1997), African American illustrator
 * W. Eugene Smith (1918–1978), American photojournalist
 * William Craig Smith (1918–1986), American art director
 * William Arthur Smith (1918–1989), American artist
 * William Jay Smith (1918–2015), American poet
 * William Gardner Smith (1927–1974), African-American novelist
 * Bill Smith (jewelry designer) (born 1933), first African American recipient of Coty Award
 * Willi Smith (1948–1987), American fashion designer
 * Will Smith, American tech journalist, 2010 founder of Tested.com

Characters

 * Bill Smith, from Canadian television series The Red Green Show, played by Rick Green
 * Billy Smith, a recurring Saturday Night Live character introduced 2003
 * Billy Smith, a character in Coronation Street
 * Will Smith (The Fresh Prince of Bel-Air), television series character
 * Will Smith (Home and Away), Australian television series character
 * Will Smith, child character in Wee Sing The Best Christmas Ever!

Music

 * Barkin' Bill Smith (1928–2000), American Chicago blues singer
 * Bill Smith (Canadian musician) (born 1938), Canadian record producer, musician, writer, editor
 * Bill Smith (English musician) (born 1940), founding member of the Quarrymen
 * Bill Smith (jazz musician) (1926–2020), folk jazz clarinetist, professor of music at the University of Washington
 * Major Bill Smith (1922–1994), American record producer and executive
 * William Smith (composer) (1603–1645), English composer from the city of Durham
 * William "Smitty" Smith (1944–1997), keyboardist and session musician
 * Willie "Big Eyes" Smith (1936–2011), blues drummer and singer
 * Willie "Long Time" Smith, dates unknown, Chicago blues pianist and singer
 * Willie Smith (alto saxophonist) (1910–1967), jazz alto saxophonist
 * Willie "the Lion" Smith (1893–1973), jazz pianist
 * William Oscar Smith, jazz double bassist and music educator

Business

 * William Henry Smith (1792–1865), entrepreneur whose business was about both newsagents and book shops
 * William Henry Smith (1825–1891), son of the above, and politician
 * William Smith (businessman) (1818–1912), nurseryman and donor to Hobart and William Smith Colleges
 * William Reardon Smith (1856–1935), British shipowner
 * Willie Reardon Smith (1887–1950), British shipowner
 * William Wensley Smith (1887–1955), founder of W. W. Smith Insurance Ltd

Law and crime

 * Sir William Cusack-Smith, 2nd Baronet (1766–1836), baronet
 * William W. Smith (Arkansas judge) (1838–1888), justice of the Arkansas Supreme Court
 * William A. Smith (Iowa judge) (1870–1958), justice of the Iowa Supreme Court
 * William A. Smith (Kansas judge) (1888–1968), Associate Justice of the Kansas Supreme Court
 * William E. Smith (judge) (born 1959), judge on the United States District Court for the District of Rhode Island
 * Sir William James Smith (1853–1912), British judge who served as the chief justice of the Supreme Court of Cyprus, British Guiana and the Transvaal
 * William Francis Smith (1904–1968), judge of the United States Court of Appeals for the Third Circuit
 * William Kennedy Smith (born 1960), physician and Kennedy family scion who was acquitted of rape in 1991
 * William Nimmo Smith, Lord Nimmo Smith (born 1942), former Senator of the College of Justice and a judge of the Supreme Courts of Scotland
 * William Owen Smith (1848–1929), lawyer involved in overthrow of the Kingdom of Hawaii
 * William Redwood Smith (1851–1935), Associate Justice of the Kansas Supreme Court
 * William Scott Smith (born 1959), American serial killer and kidnapper
 * William Smith (judge, born 1728) (1728–1793), historian, Chief Justice of the Province of New York, and Chief Justice of the Province of Quebec and later Lower Canada
 * William Smith (judge, born 1697) (1697–1769), father of John Smith, Doctor Thomas Smith, Joshua Hett Smith, and Chief Justice William Smith
 * William Smith (murderer) (1957–2005), executed by the State of Ohio in 2005
 * William "Tangier" Smith (1655–1705), Chief Justice of the Province of New York from 1692
 * William Trickett Smith (1937–2021), American lawyer who was disbarred
 * William Trickett Smith II (born 1981), his son, American drug trafficker convicted of murdering his wife in Peru in 2007

Military

 * Sir Sidney Smith (Royal Navy officer) (William Sidney Smith, 1764–1840), British admiral
 * William Smith (1746–1787), commanding officer of the Lincoln minutemen in the battles of Lexington and Concord
 * William Alexander Smith (Boys' Brigade) (1854–1914), founder of the Boys' Brigade
 * William Danvers Smith, 2nd Viscount Hambleden (1868–1928), known as Frederick Smith, officer in the British Army
 * William Douglas Smith (1865–1939), British general
 * William D. Smith (1933–2020), United States Navy admiral
 * William Duncan Smith (1825–1862), career United States Army officer
 * William Farrar Smith (1824–1903), Union Army general
 * William F. Smith (US Army Air Corps), piloted the US Army Air Corps B-25 Billy Mitchell Bomber that crashed into the Empire State Building
 * William H. Smith (Medal of Honor) (1847–1877), American Indian Wars soldier and Medal of Honor recipient
 * William James Lanyon Smith, New Zealand naval officer
 * William Osborne Smith (1833–1887), first Acting Commissioner of the North West Mounted Police
 * William Ruthven Smith (1868–1941), United States Army officer
 * William Smith (c. 1872–1941), Master of the SS Sauternes, English merchant seaman killed in World War II
 * William Smith (Medal of Honor, 1864) (1826–?), American Civil War sailor and Medal of Honor recipient
 * William Smith (Medal of Honor, 1869) (1838–?), American Indian Wars soldier and Medal of Honor recipient
 * William Smith (Royal Navy officer) (died 1756), served as Commander-in-Chief of the Jamaica Station and rose to Rear Admiral
 * William Smith (ship captain) (1768–1846), American ship captain and Revolutionary War veteran
 * William Smith (Virginia governor) (1797–1887), Governor of Virginia (1846–1849, 1864–1865) and Confederate general
 * William Sooy Smith (1830–1916), American Civil War general
 * William Thomas Smith (1896–1994), World War I flying ace
 * William Watson Smith (1892–?), World War I flying ace
 * William W. Smith (admiral) (1888–1966), United States Navy admiral during World War II
 * William Y. Smith (1925–2016), United States Air Force general

Religion

 * William Smith (minister) (died 1647), buried in the Prophet's Grave near Largs, North Ayrshire, Scotland
 * William Smith (Archdeacon of Armagh) (died 1673), English priest in Ireland
 * William Smith (Provost of St Andrew's Cathedral, Aberdeen), 18th-century Scottish priest
 * William Smith (Latter Day Saints) (1811–1893), younger brother of Joseph Smith, Jr. and himself a Mormon leader
 * William Smith (bishop) (1819–1892), Catholic archbishop of St. Andrews and Edinburgh
 * William R. Smith (Mormon) (1826–1894), Mormon leader in Davis County, Utah Territory
 * William Saumarez Smith (1836–1909), Anglican bishop/archbishop of Sydney
 * William Smith (monsignor) (1939–2009), Catholic theologian
 * William Carr Smith (1857–1930), Church of England clergyman
 * William Angie Smith (1894–1974), bishop of the Methodist Church and the United Methodist Church

Science and architecture

 * Bill Smith (Motorola engineer) (1929–1993), one of the creators of Six Sigma
 * William Gardner Smith (botanist) (1866–1928), Scottish botanist and ecologist
 * William Smith (architect) (1817–1891), Scottish architect
 * William Smith (geologist) (1769–1839), English geologist
 * William Wright Smith (1875–1956), Scottish botanist and horticulturalist
 * W. Wheeler Smith (c. 1838–c. 1908), American architect and real estate developer

American football

 * Bill Smith (American football, born 1912) (1912–1999), American football end
 * Bill Smith (American football, born 1926) (1926–2009), American football tackle and end
 * Billy Ray Smith Jr. (born 1961), American football player
 * Billy Ray Smith Sr. (1935–2001), American football player
 * Wee Willie Smith (American football) (1910–1996), American football player
 * William F. Smith (American football) (1888–?), American college football player and coach
 * Willie Smith (American football coach) (born 1931), 12th head college football coach for the North Carolina Central University Eagles
 * Willie Smith (offensive tackle, born 1937) (born 1937), former American football player
 * Willie Smith (offensive tackle, born 1986) (born 1986), American football offensive tackle
 * Willie Smith (tight end) (born 1964), American football tight end
 * Will Smith (defensive end) (1981–2016), American football defensive end
 * Will Smith (linebacker, born 1992), American football linebacker

Association football

 * Bill Smith (footballer, born 1887) (1887–1929), English footballer with Brentford, Southampton and Halifax Town
 * Bill Smith (footballer, born 1897) (1897–?), English footballer with Durham City and York City
 * Bill Smith (footballer, born 1906) (1906–1979), English footballer with Norwich City and Exeter City
 * Bill Smith (footballer, born 1926) (1926–2014), English footballer with Birmingham City and Blackburn Rovers
 * Bill Smith (footballer, born 1938), Scottish footballer with Raith Rovers and Darlington
 * Bill Smith (soccer), Canadian soccer player, active 1943–1963
 * Billy Smith (footballer, born 1872) (1872–?), English footballer with Wolverhampton Wanderers
 * Billy Smith (footballer, born 1873) (1873–1914), Scottish footballer for Newcastle United
 * Billy Smith (footballer, born 1882) (1882–?), English footballer for West Bromwich Albion and Birmingham
 * Billy Smith (footballer, born 1895) (1895–1951), English footballer with Huddersfield Town
 * Billy Smith (footballer, born 1900) (1900–?), English footballer with Hartlepool United, Huddersfield Town and Rochdale
 * Billy Smith (footballer, born 1906) (1906–1963), English footballer with South Shields, Portsmouth and Stockport County
 * Billy Smith (Scottish footballer) (c. 1931–2009), Scottish footballer with Aberdeen
 * Buxton Smith (William Smith), English footballer with Buxton and Manchester City
 * Stockport Smith (William Smith), English footballer with Stockport and Manchester United
 * William A. Smith (footballer), English footballer with Blackburn Rovers
 * William Smith (footballer, born 1865) (1865–?), English goalkeeper with Burnley
 * William Smith (footballer, born 1868) (1868–1907), English footballer with Lincoln City, Loughborough, Notts County and Nottingham Forest
 * William Smith (footballer, born 1886) (1886–1956), footballer with Bradford City and Stoke
 * William Smith (footballer, born 1903) (1903–?), English footballer
 * William Smith (Scottish footballer), footballer with Hibernian
 * Willie Smith (footballer, born 1943), Scottish footballer with Brentford
 * Willie Smith (footballer, born 1948), English footballer with Wimbledon
 * Will Smith (footballer, born 1998), English footballer for Harrogate Town
 * W. J. "Billy" Smith, football manager, Aston Villa

Baseball

 * Big Bill Smith (1869–?), Negro leagues baseball catcher and manager
 * Bill Smith (baseball executive) (born 1958), Minnesota Twins general manager
 * Bill Smith (baseball manager), National Association player-manager for the Baltimore Marylands
 * Bill Smith (pitcher) (1934–1997), American left-handed pitcher in Major League Baseball, 1958–59; 1962
 * Bill Smith (outfielder) (1865–1886), American baseball outfielder for the 1884 Cleveland Blues
 * Billy Smith (baseball coach) (born 1930), American minor league first baseman and manager and Major League coach and scout
 * Billy Smith (1980s pitcher) (born 1954), American pitcher in Major League Baseball, 1981
 * Billy Smith (1880s pitcher) (1861–1928), American right-handed pitcher in Major League Baseball, 1886
 * Billy Smith (second baseman) (born 1953), American infielder in Major League Baseball, 1975–79; 1981
 * Willie Smith (outfielder) (1939–2006), American outfielder in Major League Baseball, 1963–1971
 * Willie Smith (third baseman), American third baseman in Negro league baseball, 1938
 * Willie Smith (1940s pitcher), American pitcher in Negro league baseball, 1948
 * Willie Smith (1990s pitcher) (born 1967), American pitcher in Major League Baseball, 1994
 * Will Smith (pitcher) (born 1989), American pitcher in Major League Baseball
 * Will Smith (catcher) (born 1995), American baseball catcher
 * Dark Night Smith (William C. Smith), American pitcher in Negro league baseball, 1920–1924

Basketball

 * Bill Smith (basketball, born 1939), American basketball player
 * Wee Willie Smith (1911–1992), American basketball player
 * William Smith (basketball, born 1949), American basketball player
 * Willie Smith (basketball) (born 1953), American professional basketball player

Cricket

 * Bill Smith (cricketer) (1937–2018), English cricketer
 * William Brook-Smith (1885–1952), New Zealand cricketer
 * William Smith (cricketer, born 1839) (1839–1897), first class cricketer for Yorkshire
 * William Smith (cricketer, born 1875) (1875–1942), first-class cricketer for London County
 * William Smith (cricketer, born 1882) (1882–?), English cricketer
 * William Smith (cricketer, born 1900) (1900–1990), English cricketer
 * William Smith (cricketer, born 1902) (1902–1937), Scottish cricketer
 * William Smith (Kent cricketer) (1819–1883), English cricketer
 * William Smith (Somerset cricketer) (1871–1946), English cricketer
 * Willie Smith (cricketer) (1885–1964), English cricketer
 * Will Smith (cricketer) (born 1982), English cricketer

Rugby football

 * Bill Smith, Australian rugby league footballer in the Bulimba Cup
 * Bill Smith, rugby league right wing of the 1950s for Whitehaven
 * Billy Smith (rugby league, born 1942), Australian rugby league player
 * Billy Smith (rugby league, born 1999), Australian rugby league player
 * W. Smith (rugby league) (active 1908–1912), Australian rugby league player
 * Will Smith (rugby league) (born 1992), Australian rugby league player
 * William Smith (rugby union) (1881–1945), New Zealand rugby union player

Other sports

 * Bill Smith (Australian rules footballer) (1936–2010), Australian rules footballer for Fitzroy
 * Billy Smith (Australian footballer) (1894–1953), played with North Melbourne in the Victorian Football League
 * Bill Smith (fell runner) (1936–2011), fell runner and author on the sport
 * Bill Smith (motorcyclist) (born 1935), former Grand Prix motorcycle road racer
 * Bill Smith (poker player) (1934–1996), professional poker player
 * Bill Smith (swimmer) (1924–2013), two-time gold medalist in the 1948 Olympic games
 * Billy Dee Smith (born 1982), professional lacrosse player
 * Billy Smith (ice hockey) (born 1950), Canadian ice hockey goaltender
 * Mysterious Billy Smith (1871–1937), Canadian boxer
 * Will Smith (ice hockey) (born 2005), American ice hockey forward
 * William Alexander Smith (boxer) (1904–1955), South African boxer of the 1920s
 * William Smith (cyclist) (1893–1958), South African Olympic cyclist
 * William Smith (ice hockey) (born 2005), American hockey player
 * William Smith (field hockey) (1886–1937), British field hockey player who competed in the 1920 Summer Olympics
 * William Smith (golfer) (1865–1936), American golfer
 * William Smith (sport shooter) (1877–1953), Canadian Olympic sport shooter
 * William Smith (wrestler) (1928–2018), 1952 Olympic gold medalist
 * Willie Smith (billiards player) (1886–1982), English professional player of snooker and English billiards
 * Willie Smith (golfer) (1876–1916), Scottish golfer
 * Willie Smith (hurdler) (born 1977), Namibian track and field hurdler
 * Willie Smith (sprinter) (1956–2020), American 400 metres runner

Australia

 * William Collard Smith (1830–1894), treasurer in colonial Victoria (Australia)
 * William Laird Smith (1869–1942), Australian representative for Denison, 1910–1922 and Minister for the Navy, 1920–1921
 * William Forgan Smith (1887–1953), Premier of the Australian state of Queensland, 1932–1942
 * William Kennedy Smith (Australian politician) (1888–1933)

Canada

 * William Smith (Nova Scotia politician) (died 1779), merchant, judge and politician in Nova Scotia
 * Amor De Cosmos (William Alexander Smith, 1825–1897), Premier of British Columbia
 * William Henry Smith (Canadian politician) (1826–1890), lawyer and political figure in Nova Scotia, Canada
 * William Smith (Canadian politician) (1847–1931), member of Canadian House of Commons 1887–1921
 * William C. Smith (politician) (1875–1968), politician from Alberta, Canada
 * William Haslam Smith (1891–?), businessman and political figure in Nova Scotia, Canada
 * William Duncan Smith (politician) (1899–1977), Canadian politician in the Legislative Assembly of British Columbia
 * Bill Smith (Alberta politician) (born 1935), former mayor of Edmonton
 * William Smith (Newfoundland politician) (1910–1965), politician in Newfoundland
 * J. William Smith, member of the Legislative Assembly of New Brunswick

New Zealand

 * William Mein Smith (1798–1869), key actor in the early settlement of New Zealand's capital city, Wellington
 * William Cowper Smith (1843–1911), Liberal Party Member of Parliament in New Zealand

United Kingdom

 * William Goldsmith alias Smith (died 1517), MP for Gloucester
 * William Smith (fl. 1553–54), MP for Newport (Cornwall)
 * William Smith (died 1591), MP for Wells
 * William Smith (MP for Ripon) (1550–1626), MP for Ripon
 * William Smith (MP for Aylesbury) (1568–1620), MP for Aylesbury, 1604
 * William Smith (surveyor), fl 1726
 * William Smith (Ordnance) (1721–1803), of Chichester, UK, Treasurer of the Ordnance
 * William Smith (abolitionist) (1756–1835), grandfather of Florence Nightingale, dissenter and British MP
 * William Smith of Carbeth Guthrie (1787–1871), Lord Provost of Glasgow
 * William Henry Smith (1825–1891), MP and Cabinet Minister (First Lord of the Admiralty, War Secretary)
 * William Masters Smith (1802–1861), Member of Parliament for West Kent
 * William Smith (1849–1913), Member of Parliament for North Lonsdale, 1892–1895
 * William Smith, 3rd Viscount Hambleden (1903–1948), British peer
 * William Smith, 4th Viscount Hambleden (1930–2012), British peer
 * William Smith (loyalist) (1954–2016), Northern Irish loyalist politician

United States

 * William Smith (Delaware politician), state politician from Delaware
 * William Smith (Maryland politician) (1728–1814), member of the U.S. House of Representatives from Maryland (1789–1791)
 * William Smith (New York state senator) (1720–1799), New York politician and judge
 * William Smith (Oregon politician), Oregon state senator (1890s)
 * William Smith (South Carolina representative) (1751–1837), member of the U.S. House of Representatives from South Carolina (1797–1798)
 * William Smith (South Carolina senator) (1762–1840), U.S. senator from South Carolina (1815–1830)
 * William Smith (Virginia governor) (1797–1887), Governor of Virginia (1846–1849, 1864–1865) and Confederate general
 * William Smith (Virginia representative), member of the U.S. House of Representatives from Virginia (1821–1827)
 * William Alden Smith (1859–1932), member of the U.S. House of Representatives (1895–1906) and U.S. Senator (1905–1918) from Michigan
 * William Alexander Smith (politician) (1828–1888), member of the U.S. House of Representatives from North Carolina (1873–1874)
 * William Burns Smith (1844–1917), mayor of Philadelphia
 * William C. Smith Jr. (born 1982), Maryland State legislator
 * William E. Smith (politician) (1824–1883), Governor of Wisconsin (1878–1882)
 * William Ephraim Smith (1829–1890), member of the Confederate (1863–1865) and U.S. (1875–1881) House of Representatives from Georgia
 * William Ernest Smith (1890–1973), mayor of Murray, Utah, 1946–1947
 * William F. Smith (New York politician) (1901–1950), member of the New York State Assembly (1926–1933)
 * William French Smith (1917–1990), U.S. Attorney General (1981–1985)
 * William Grover Smith (1857–1921), Lieutenant Governor of Colorado, 1889–1891
 * William H. Smith (Connecticut politician) (1842–1915), warden of the Borough of Norwalk, Connecticut
 * William Henry Smith (American politician) (1833–1896), newspaper editor and politician, Ohio Secretary of State 1865–1868
 * William Hugh Smith (1826–1899), governor of Alabama (1868–1870)
 * William J. Smith (Maryland politician) (1850–1906), American politician
 * William Jay Smith (Tennessee politician) (1823–1913), member of the U.S. House of Representatives from Tennessee
 * William L. Smith (barber) (1878–?), Socialist barber from Milwaukee who served three terms in the Wisconsin State Assembly
 * William Loughton Smith (1758–1812), member of the U.S. House of Representatives from South Carolina (1789–1798)
 * William Lyman Smith (1878–1964), telephone businessman who served one term in the Wisconsin State Assembly and two in the Wisconsin State Senate
 * William M. Smith, Speaker of the Illinois House of Representatives
 * William N. H. Smith (1812–1889), member of the U.S. House of Representatives from North Carolina (1859–1860)
 * William Orlando Smith (1859–1932), member of the U.S. House of Representatives from Pennsylvania (1903–1906)
 * William R. Smith (Mormon) (1826–1894), member of the Utah Territory House of Representatives
 * William Robert Smith (1863–1924), member of the U.S. House of Representatives from Texas (1903–1916)
 * William Rudolph Smith (1787–1868), politician in the states of Pennsylvania and Wisconsin
 * William Russell Smith (1815–1896), member of the U.S. House of Representatives from Alabama (1851–1856)
 * William Stephens Smith (1755–1816), member of the U.S. House of Representatives from New York (1813–1816) and son-in-law of President John Adams
 * William T. Smith (1916–2010), member of the New York State Senate

Other persons

 * William Smith (conservationist) (1852–1942), New Zealand gardener, naturalist and conservationist
 * William Smith (shearer) (1896–1947), perhaps the most skilled sheep-shearer in the first half of the 20th century
 * William Smith (mariner) (1790–1847), British mariner and discoverer of the South Shetland Islands
 * William Smith (physician), Scottish American physician
 * William Smith (registrar) (1816–1895), Ghanaian civil servant
 * William Crawford Smith (1837–1899), American architect
 * William R. Smith (physician) (born 1973), American emergency physician and wilderness medicine consultant
 * William Robert Smith (physician) (1850–1932), British public health expert
 * William Tyler Smith (1815–1873), English obstetrician, medical writer and journalist
 * William Wragg Smith (1808–1875), American planter, lawyer, naturalist, translator and poet

title: William Smith


text:
Adair County, Iowa

Adair County is a county in the U.S. state of Iowa. As of the 2020 census, the population was 7,496. Its county seat is Greenfield.

History
Adair County was formed in 1851 from sections of Pottawattamie County. It was named for John Adair, a general in the War of 1812, and the eighth Governor of Kentucky.

Geography
According to the U.S. Census Bureau, the county has a total area of 570 sqmi, of which 569 sqmi is land and 1.0 sqmi (0.2%) is water.

Major highways

 * [[Image:I-80.svg|x20px]] Interstate 80
 * [[Image:US 6.svg|x20px]] U.S. Highway 6
 * [[Image:Elongated circle 25.svg|x20px]] Iowa Highway 25
 * [[Image:Elongated circle 92.svg|x20px]] Iowa Highway 92

Adjacent counties

 * Guthrie County (north)
 * Madison County (east)
 * Union County (southeast)
 * Adams County (southwest)
 * Cass County (west)

Demographics

2020 census
The 2020 census recorded a population of 7,496 in the county, with a population density of. 96.88% of the population reported being of one race. 92.89% were non-Hispanic White, 0.61% were Black, 2.48% were Hispanic, 0.25% were Native American, 0.31% were Asian, 0.03% were Native Hawaiian or Pacific Islander and 3.43% were some other race or more than one race. There were 3,585 housing units of which 3,217 were occupied.

2010 census
As of the 2010 United States Census, there were 7,682 people, 3,292 households, and 2,148 families residing in the county. The population density was 13.5 PD/sqmi. There were 3,698 housing units at an average density of 6.5 /sqmi. The racial makeup of the county was 98.4% white, 0.3% Asian, 0.1% American Indian, 0.1% black or African American, 0.4% from other races, and 0.7% from two or more races. Those of Hispanic or Latino origin made up 1.3% of the population. In terms of ancestry, 42.9% were German, 12.6% were Irish, 11.9% were English, 6.7% were Danish, and 6.4% were American.

Of the 3,292 households, 26.8% had children under the age of 18 living with them, 54.9% were married couples living together, 6.7% had a female householder with no husband present, 34.8% were non-families, and 30.7% of all households were made up of individuals. The average household size was 2.29 and the average family size was 2.84. The median age was 45.3 years.

The median income for a household in the county was $45,202 and the median income for a family was $57,287. Males had a median income of $38,638 versus $31,642 for females. The per capita income for the county was $23,497. About 5.7% of families and 10.6% of the population were below the poverty line, including 13.5% of those under age 18 and 11.4% of those age 65 or over.

Religion
, 67.9% of the population (5,597) had a declared religious affiliation, in every case Christian. The leading religious denomination was the United Methodist Church, with 23.6% of the population (1,944 members); second was the Lutheran Church–Missouri Synod, with 15.4% (1,268 members); third was the Roman Catholic church, with 12% of the population (1,003 members); and fourth was the Evangelical Lutheran church, with 11.8% of the population (978 members).

Education
The county is served by five school districts:
 * Nodaway Valley Community School District
 * Orient-Macksburg Community School District.
 * CAM Community School District
 * Adair–Casey Community School District.
 * West Central Valley Community School District

The schools in the Nodaway Valley Community School District are:
 * Nodaway Valley Elementary School
 * Nodaway Valley Middle School
 * Nodaway Valley High School.

The schools in the Orient-Macksburg Community School District are: The schools in the CAM Community School District are:
 * Orient-Macksburg Elementary School
 * Orient-Macksburg Middle School and High School.

 * CAM North Elementary School
 * CAM South Elementary School
 * CAM Middle School
 * CAM High School
 * CAM Iowa Connections Academy Elementary
 * CAM Iowa Connections Academy Middle School
 * CAM Iowa Connections Academy High School

The schools in the Adair–Casey Community School District are:

 * Adair–Casey Elementary School
 * AC/GC Junior High School
 * Under a grade-sharing relationship with Guthrie Center Community School District, students attend AC/GC High School in Guthrie Center.

The schools in the West Central Valley Community School District are:

 * Dexter Elementary School
 * Stuart Elementary School
 * Redfield Middle School
 * Stuart High School

Cities

 * Adair
 * Bridgewater
 * Casey
 * Fontanelle
 * Greenfield
 * Orient
 * Stuart

Townships
Adair County is divided into sixteen townships:

 * Eureka
 * Grand River
 * Grove
 * Harrison
 * Jackson
 * Jefferson
 * Lee
 * Lincoln
 * Orient
 * Prussia
 * Richland
 * Summerset
 * Summit
 * Union
 * Walnut
 * Washington

Population ranking
The population ranking of the following table is based on the 2020 census of Adair County.

† county seat

Politics
The county was part of Iowa's 5th congressional district, which had a score of R+9 (strongly Republican) in the Cook Partisan Voting Index.

title: Adair County, Iowa


text:
Alcohol proof

Alcohol proof (usually termed simply "proof" in relation to a beverage) is a measure of the content of ethanol (alcohol) in an alcoholic beverage. The term was originally used in England and from 1816 was equal to about 1.75 times the percentage of alcohol by volume (ABV). The United Kingdom today uses ABV instead of proof. In the United States, alcohol proof is defined as twice the percentage of ABV. The definition of proof in terms of ABV varies from country to country.

The measurement of alcohol content and the statement of content on bottles of alcoholic beverages is regulated by law in many countries. In 1972, Canada phased out the use of "proof"; in 1973, the European Union followed suit; and the United Kingdom, where the concept originated, started using ABV instead in 1980. The United States Code mandates the use of ABV, but permits proof to be used also.

The degree symbol (°) is sometimes used to indicate alcohol proof, either alone (e.g. 10°) or after a space and joined to the letter P as a unit name (e.g. 13 °P).

History
The term proof dates back to 16th century England, when spirits were taxed at different rates depending on their alcohol content. Similar terminology and methodology spread to other nations as spirit distillation, and taxation, became common. In England, spirits were originally tested with a basic "burn-or-no-burn" test, in which an alcohol-containing liquid that would ignite was said to be "above proof", and one which would not was said to be "under proof". A liquid just alcoholic enough to maintain combustion was defined as 100 proof and was the basis for taxation. Because the flash point of alcohol is highly dependent on temperature, 100 proof defined this way ranges from 20% at 36 C to 96% at 13 C alcohol by (ABW); at 24 C 100 proof would be 50% AB.

Another early method for testing liquor's alcohol content was the "gunpowder method". Gunpowder was soaked in a spirit, and if the gunpowder could still burn, the spirit was rated above proof. This test relies on the fact that potassium nitrate (a chemical in gunpowder) is significantly more soluble in water than in alcohol. While less influenced by temperature than the simpler burn-or-no-burn test, gunpowder tests also lacked true reproducibility. Factors including the grain size of gunpowder and the time it sat in the spirit impact the dissolution of potassium nitrate and therefore what would be defined as 100 proof. However, the gunpowder method is significantly less variable than the burn-or-no-burn method, and 100 proof defined by it is traditionally defined as 57.15% ABV.

By the end of the 17th century, England had introduced tests based on specific gravity for defining proof. However, it was not until 1816 that a legal standard based on specific density was defined in England. 100 proof was defined as a spirit with $12/13$ the specific gravity of pure water at the same temperature. From the 19th century until 1 January 1980, the UK officially measured alcohol content by proof spirit, defined as spirit with a gravity of $12/13$ that of water, or 923 kg/m3, and equivalent to 57.15% ABV.

The value 57.15% is very close to the fraction $4/7$ ≈ 0.5714. This led to the approximation that 100-proof spirit has an ABV of $4/7$. From this, it follows that to convert the ABV expressed as a percentage to degrees proof, it is only necessary to multiply the ABV by $7/4$. Thus pure 100% alcohol will have 100×($7/4$) = 175 proof, and a spirit containing 40% ABV will have 40×($7/4$) = 70 proof.

The proof system in the United States was established around 1848 and was based on percent alcohol rather than specific gravity. Fifty percent alcohol by volume was defined as 100 proof. Note that this is different from 50% volume fraction (expressed as a percentage); the latter does not take into account change in volume on mixing, whereas the former does. To make 50% ABV from pure alcohol, one would take 50 parts of alcohol and dilute to 100 parts of solution with water, all the while mixing the solution. To make 50% alcohol by volume fraction, one would take 50 parts alcohol and 50 parts water, measured separately, and then mix them together. The resulting volume will not be 100 parts but between 96 and 97 parts, since the smaller water molecules can take up some of the space between the larger alcohol molecules (see volume change).

The use of proof as a measure of alcohol content is now mostly linguistic and historical. Today, liquor is sold in most locations with labels that state its percentage alcohol by volume.

European Union
The European Union (EU) follows recommendations of the International Organization of Legal Metrology (OIML). OIML's International Recommendation No. 22 (1973) provides standards for measuring alcohol strength by volume and by mass. A preference for one method over the other is not stated in the document, but if alcohol strength by volume is used, it must be expressed as a percentage of total volume, and the water/alcohol mixture must have a temperature of 20 C when measurement is done. The document does not address alcohol proof or the labeling of bottles.

United Kingdom
On 1 January 1980, Britain adopted the ABV system of measurement prescribed by the European Union, of which it was then a member. The OIML recommendation for ABV used by the EU states the alcohol by volume in a mixture containing alcohol as a percentage of the total volume of the mixture at a temperature of 293.15 K. It replaced the Sikes hydrometer method of measuring the proof of spirits, which had been used in Britain for over 160 years.

United States
In the United States, alcohol content is legally mandated to be specified as an ABV percentage. For bottled spirits over 100 ml containing no solids, actual alcohol content is allowed to vary by up to 0.15% of the ABV stated on the label. By contrast, bottled spirits which are less than 100 ml (as well as those which otherwise contain solids) may vary by up to 0.25%. Proof (the term degrees proof is not used), defined as being twice the percentage of alcohol by volume, may be optionally stated in conjunction with the ABV. For example, whisky may be labeled as 50% ABV and as 100 proof; 86-proof whisky contains 43% ABV. The most typical bottling proof for spirits in the United States is 80 US proof, and there is special legal recognition of 100-proof spirits in the bottled in bond category defined since 1897.

The Code of Federal Regulations requires that liquor labels state the percentage of ABV. The regulation permits, but does not require, a statement of the proof, provided that it is printed close to the ABV number. In practice, proof levels continue to be stated on nearly all spirits labels in the United States, and are more commonly used than ABV when describing spirits in journalism and informal settings.

Canada
Beverages were labelled by alcohol proof in Canada until 1972, then replaced by ABV.

title: Alcohol proof


text:
Talk:Bifurcation diagram

unstable solutions
The article claims that it is customary to show the unstable solutions as dotted lines, however the image is missing a number of unstable solutions (namely (r-1)/r). Can it be added please? — Preceding unsigned comment added by 68.173.18.226 (talk) 15:22, 4 September 2011 (UTC)

Deleted
I have deleted most of this text since it was about the logistic map or about the mandelbrot set, but not about bifurcation diagrams and most of its contents was already contained under logistic map. I am not an expert on dynamical systems, so I hope someone else can write the appropriate article for this title. --Lenthe 16:29, 17 Jun 2005 (UTC)

When Xn+1 = R Xn another good way to show the stable points is to plot Xn+1 as function of Xn, with Excel it is easy to do, it can be verified that the system is chaotic when R is slightly higher than 3,57  (it will become non chaotic for higher values of R)

by Dingy, July 2005, figures homemade, can be used in the text

 * An important theorem about bifurcation diagrams is Sarkovskii's theorem, summarized as "Period three implies chaos".

Sarkovskii's theorem is not about bifurcation diagrams, since it doesn't say anything about how the cycle structure changes as the parameter is varied. Also "Period three implies chaos" is not Sarkovskii's theorem, and does not follow from it. AxelBoldt 02:17 Sep 30, 2002 (UTC)

The order in which the cycles first appear, starting with the 1-cycle and ending with the 3-cycle, is the same as Sarkovskii's order backward. "Period Three Implies Chaos" is by James Yorke. I haven't read it, but according to Chaos by James Gleick, when Yorke was in Berlin, Sarkovskii came up to him and told him that he had proved the same result. -phma

The diagram shown here is not a bifurcation diagram. It is an orbit diagram (which is unfortunately sometimes incorrectly referred to as a bifurcation diagram). A bifurcation diagram shows all cycles, attracting or otherwise, and does not include points that have not yet converged to a cycle, since it is not generated by iteration. I know of a good reference that explains the difference and has examples of both. I will try to find it. CyborgTosser (Only half the battle) 09:05, 26 Apr 2005 (UTC)

Here it is. CyborgTosser (Only half the battle) 01:47, 27 Apr 2005 (UTC)

Sarkovskii's theorem says that "period three" implies an infinity of periodic orbits, which is often one of the defining characteristics of chaos. However, this doesn't really have anything to do with bifurcation diagrams. This pages should perhaps contain bifurcation diagrams for the three simple local bifurcations (saddle-node, transcritical and pitchfork) and perhaps also for the Hopf bifurcation. The logistic map diagram is not a complete bifurcation diagram because it does not contain the unstable solutions after each of the period-doubling bifurcations, althought it is often referred to as such. Mathmoclaire 05:14, 13 May 2006 (UTC)

Rewrite
I'm going to try and attempt to rewrite this page, as currently it's not really about bifurcation diagrams per se. If anyone has any comments or would like to help, that would be great. Mathmoclaire 13:19, 29 July 2006 (UTC)

Which image is better?

The one on the top is better because it uses more iterations for every value of the parameter r; it then uses shades of grey to indicate which regions are visited most frequently. The picture is also bigger. On the other hand, the description of the bottom picture has some Octave code which may be useful. -- Jitse Niesen (talk) 03:12, 19 April 2007 (UTC)

 * It would be nice if the first one had source code...  I don't understand the obsession with deleting all unused images ASAP. — Omegatron 14:47, 19 April 2007 (UTC)

external links and references missing
Please add some!Lakinekaki 21:11, 19 April 2007 (UTC)

As an example: For x(n+1) = x(n).^2 -c; the code in Matlab can be written as [...]
 * This is NOT an Matlab term for the logistic map with which the example started, right?

The bifurcation diagram nicely shows [...]
 * I don't see a diagram for the Matlab example currently in the article. Maybe someone can generate one?

Thanks, --Abdull (talk) 08:43, 4 July 2008 (UTC)

Edge of chaos
3.739 is P5. The edge of chaos where order is to the left and chaos is to the right is greater than 3.74432 but equal or less than 3.74433. -32ieww 10:09PM 11/19/2015 NY time 32ieww (talk) 03:09, 20 November 2015 (UTC)

Actually 3.74432 has the occasional aperodic burst. According to my program the first one happens at about step 19000. -32ieww 10:14PM 11/19/2015 NY time 32ieww (talk) 03:14, 20 November 2015 (UTC)

title: Talk:Bifurcation diagram