astronomy

John A. Thorpe

John A. Thorpe is a astronomy 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 A. Thorpe rather than just read about it. In short: John Alden Thorpe (February 29, 1936 – January 18, 2021) was an American mathematician, known for contributions to the field of differential geometry. Thorpe obtained his Bachelor's degree in 1958 from the Massachusetts Institute of Technology.

Key takeaways

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

Reference excerpt

John Alden Thorpe (February 29, 1936 – January 18, 2021) was an American mathematician, known for contributions to the field of differential geometry. Thorpe obtained his Bachelor's degree in 1958 from the Massachusetts Institute of Technology. His Ph.D. was done at Columbia University, under the direction of James Eells (Higher Order Sectional Curvature). From 1963 to 1965, he was Moore Instructor at MIT and Assistant Professor at Haverford College in 1965. In 1967 and 1968 he was a visitor at the Institute for Advanced Study. From 1968, he was Associate Professor and then Professor at the State University of New York at Stony Brook (SUNY). From 1987 he was Professor and Dean at the State University of New York in Buffalo, and from 1993 at Queens College of City University of New York, where he also served as Provost. From 1984 to 1987 he served on the Board of Governors of the Mathematical Association of America. From 1998 to 2001 he was Executive Director of the National Council of Teachers of Mathematics. He and Nigel Hitchin independently found an inequality between topological invariants, which provides a necessary condition for the existence of Einstein metrics on four-dimensional smooth compact manifolds. It is now known as the Hitchin-Thorpe inequality. Thorpe died on January 18, 2021, at the age of 84.

Books Lecture Notes on Elementary Topology and Geometry (with I.M. Singer), Springer Verlag, Undergraduate Texts in Mathematics, 1967 Linear Algebra, with Applications to Differential Equations (with Paul G. Kumpel), Holt, Rinehart and Winston, 1971 Elementary Topics in Differential Geometry, Springer Verlag, Undergraduate Texts in Mathematics, 1979 Elementary Linear Algebra (with Paul G. Kumpel), Saunders College Publishing, 1984

References

Worked examples

Example 1 — a first encounter with John A. Thorpe

Start with the simplest possible case. Write down what John A. Thorpe claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 A. Thorpe 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 A. Thorpe 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 A. Thorpe

In research: John A. Thorpe appears in astronomy 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 A. Thorpe 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 A. Thorpe is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1936 births, 2021 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for John A. Thorpe 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 A. Thorpe in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what John A. Thorpe 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 A. Thorpe out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is John A. Thorpe in simple terms?

Why does John A. Thorpe matter?

Because it connects several astronomy 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 A. Thorpe?

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 A. Thorpe.