mathematics

John Wrench

John Wrench 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 John Wrench rather than just read about it. In short: John William Wrench, Jr. (October 13, 1911 – February 27, 2009) was an American mathematician who worked primarily in numerical analysis.

Key takeaways

John Wrench belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect John Wrench to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of John Wrench from memory before moving on to harder problems.

Reference excerpt

John William Wrench, Jr. (October 13, 1911 – February 27, 2009) was an American mathematician who worked primarily in numerical analysis. He was a pioneer in using computers for mathematical calculations, and is noted for work done with Daniel Shanks to calculate the mathematical constant pi to 100,000 decimal places.

Life and education Wrench was born on October 13, 1911, in Westfield, New York, and grew up in Hamburg, New York. He received a BA summa cum laude in mathematics in 1933 and an MA in mathematics in 1935, both from the University at Buffalo. He received his PhD in mathematics in 1938 from Yale University. His thesis was titled The derivation of arctangent relations. Wrench died on February 27, 2009, of pneumonia in Frederick, Maryland.

Career Wrench started his career teaching at George Washington University, but switched to doing research for the United States Navy during World War II. His specialty for the Navy was developing high-speed computational methods, and he was a pioneer in using computers for mathematical calculations. He worked on projects involving underwater sound waves, underwater explosions, structural design, hydrodynamics, aerodynamics, and data analysis. He became deputy head of the Applied Mathematics Laboratory at the Navy's David Taylor Model Basin in 1953, and retired in 1974 as the head of the laboratory. He also had academic appointments at Yale University, Wesleyan University, University of Maryland, College Park, and American University. Wrench had a particular interest in computing the decimal digits of π, and performed some lengthy calculations even before the availability of computers. During the period 1945–1956 Wrench and Levi B. Smith used a desk calculator to produce more and more digits of π, ending with 1160 places. In 1961, Wrench and Daniel Shanks used an IBM 7090 computer to calculate π to 100,000 digits. Harry Polachek had a printout of the 100,000 digits specially bound, inscribed in gold letters, and donated to the Smithsonian Institution. Wrench also calculated a number of other mathematical constants to high precision, for example the Euler–Mascheroni constant γ to 328 decimal places and Khinchin's constant to 65 places. He was the editor of the Journal of Mathematics of Computation from 1959 to 1978. Wrench was a member of the National Academy of Sciences and the National Research Council. He published more than 150 scientific papers.

Notes

External links John Wrench at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with John Wrench

Start with the simplest possible case. Write down what John Wrench 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 John Wrench 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 John Wrench 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 John Wrench

In research: John Wrench 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 John Wrench 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: John Wrench is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1911 births, 2009 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for John Wrench 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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How to study John Wrench in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what John Wrench means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain John Wrench out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is John Wrench in simple terms?

John William Wrench, Jr. (October 13, 1911 – February 27, 2009) was an American mathematician who worked primarily in numerical analysis.

Why does John Wrench 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 John Wrench?

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.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on John Wrench.