mathematics

William Francis Pohl

William Francis Pohl is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand William Francis Pohl rather than just read about it. In short: William Francis Pohl (16 September 1937 – 9 December 1988) was an American mathematician, specializing in differential geometry and known for the Clifton–Pohl torus. Pohl received from the University of Chicago his B.A in 1957 and his M.A.1958.

Key takeaways

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Reference excerpt

William Francis Pohl (16 September 1937 – 9 December 1988) was an American mathematician, specializing in differential geometry and known for the Clifton–Pohl torus. Pohl received from the University of Chicago his B.A in 1957 and his M.A.1958. He completed his Ph.D. at Berkeley in 1961 under the direction of Shiing-Shen Chern with dissertation Differential Geometry of Higher Order. His dissertation was published in 1962 in the journal Topology and has received over 120 citations in the mathematical literature. He was a member of the mathematics faculty at the University of Minnesota from September 1964 until his untimely death. Pohl engaged in a famous controversy arguing against Francis Crick but, in view of additional empirical evidence, conceded about 1979 or 1980 that Crick was correct. Pohl sang liturgical music in Catholic religious services and wrote an article in 1966 from which the journal Sacred Music published an excerpt in 2011.

In the early 1970s, Dr. William F. Pohl, a professor of mathematics at the University of Minnesota, sang the Gregorian chant, mostly solo, while developing a small schola of Chorale volunteers to assist him. Dr. Pohl guided the chant during the aftermath of the Second Vatican Council when all the liturgical books were being revised ? no small task, but as some may recall, he was no small man. By 1975, in cooperation with Monsignor Richard J. Schuler, pastor of Saint Agnes, and Harold Hughesdon, its master of ceremonies, Dr. Pohl, joined by a number of dedicated volunteers, had begun the custom of singing Sunday vespers weekly and the full office of Tenebrae during Holy Week.

Organist David Bevan arrived from England in 1976 to accompany the Chorale, and he assumed directorship of the Gregorian chant after Dr. Pohl's retirement in 1977.William Pohl later married Hildegard Bastian (now Hildegard Pohl), and fathered 5 children, Annetta Pohl, Agatha Pohl, Agnes Pohl, Lawrence Pohl, and John Pohl.

Selected publications Pohl, William F. (1966). "Connexions in differential geometry of higher order". Transactions of the American Mathematical Society. 125 (2): 310–325. doi:10.1090/s0002-9947-1966-0203628-1. JSTOR 1994357. "The self-linking number of a closed space curve (Gauss integral formula treated for disjoint closed space curves linking number)" (PDF). Journal of Mathematics and Mechanics. 17: 975–985. 1968. Pohl, William F. (1968). "Some integral formulas for space curves and their generalization". American Journal of Mathematics. 90 (4): 1321–1345. doi:10.2307/2373302. JSTOR 2373302. with T. F. Banchoff: Banchoff, Thomas F.; Pohl, William F. (1971). "A generalization of the isoperimetric inequality". Journal of Differential Geometry. 6 (2): 175–192. doi:10.4310/jdg/1214430403. MR 0305319. with John Alvord Little: Little, John A.; Pohl, William F. (1971). "On tight immersions of maximal codimension" (PDF). Inventiones Mathematicae. 13 (3): 179–204. Bibcode:1971InMat..13..179L. doi:10.1007/BF01404629. hdl:2027.42/46589. S2CID 54785966. with Nicolaas H. Kuiper: Kuiper, Nicolaas H.; Pohl, William F. (1977). "Tight topological embeddings of the real projective plane in E5 ". Inventiones Mathematicae. 42 (1): 177–199. Bibcode:1977InMat..42..177K. doi:10.1007/BF01389787. S2CID 120800935. Pohl, William F. (1981). "The probability of linking of random closed curves". Geometry Symposium Utrecht 1980. Lecture Notes in Mathematics. Vol. 894. Springer Berlin Heidelberg. pp. 113–126. doi:10.1007/BFb0096227. ISBN 978-3-540-11167-2.

References

Worked examples

Example 1 — a first encounter with William Francis Pohl

Start with the simplest possible case. Write down what William Francis Pohl claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to William Francis Pohl before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about William Francis Pohl ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of William Francis Pohl

In research: William Francis Pohl appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses William Francis Pohl in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: William Francis Pohl is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1937 births, 1988 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for William Francis Pohl outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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Frequently asked questions

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Why does William Francis Pohl matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study William Francis Pohl?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

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It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on William Francis Pohl.