mathematics

Leonard Blumenthal

Leonard Blumenthal 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 Leonard Blumenthal rather than just read about it. In short: Leonard Mascot Blumenthal (February 27, 1901 – August 1984) was a Jewish American mathematician. Career He received his Ph.D. in 1927 from Johns Hopkins University, under the supervision of Frank Morley; his dissertation was titled Lagrange Resolvents in Euclidean Geometry.

Key takeaways

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

Reference excerpt

Leonard Mascot Blumenthal (February 27, 1901 – August 1984) was a Jewish American mathematician.

Career He received his Ph.D. in 1927 from Johns Hopkins University, under the supervision of Frank Morley; his dissertation was titled Lagrange Resolvents in Euclidean Geometry. He taught for the majority of his professional career at the University of Missouri and was the author of A Modern View of Geometry. He was a visiting scholar at the Institute for Advanced Study from 1933 to 1936. According to the Mathematics Genealogy Project, he had 18 Ph.D. students at Missouri, among them Leroy Milton Kelly and William Arthur Kirk; he is the academic ancestor of over 80 mathematicians.

Legacy The Leonard M. Blumenthal Distinguished Professorship in Mathematics at the University of Missouri was established in 1992 in honor of Blumenthal. This endowed chair is given on a five-year rotating basis to Missouri mathematics professors; the Blumenthal Professors at Missouri have included John Beem, Mark Ashbaugh, Alex Koldobsky, and Zhenbo Qin. The American Mathematical Society also issued the Blumenthal Award in his honor.

References

Works Blumenthal L.M. Theory and applications of distance geometry (1953), Oxford: At the Clarendon Press (Geoffrey Cumberlege), XI, 347 p. Blumenthal L.M. Theory and applications of distance geometry, (2nd edition, 1970), Bronx, New York: Chelsea Publishing Company. XI, 347 p., ISBN 0-8284-0242-6 Blumenthal L.M. A Modern View of Geometry (1961), W. H. Freeman & Co.; Dover edition (1980) ISBN 0-486-63962-2

External links Leonard Blumenthal at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Leonard Blumenthal

Start with the simplest possible case. Write down what Leonard Blumenthal 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 Leonard Blumenthal 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 Leonard Blumenthal 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 Leonard Blumenthal

In research: Leonard Blumenthal 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 Leonard Blumenthal 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: Leonard Blumenthal is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1901 births, 1984 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Leonard Blumenthal 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 Leonard Blumenthal in 20 minutes

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

Frequently asked questions

What is Leonard Blumenthal in simple terms?

Leonard Mascot Blumenthal (February 27, 1901 – August 1984) was a Jewish American mathematician. Career He received his Ph.D. in 1927 from Johns Hopkins University, under the supervision of Frank Morley; his dissertation was titled Lagrange Resolvents in Euclidean Geometry.

Why does Leonard Blumenthal 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 Leonard Blumenthal?

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 Leonard Blumenthal.