astronomy

Lloyd Dines

Lloyd Dines 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 Lloyd Dines rather than just read about it. In short: Lloyd Lyne Dines (29 March 1885, in Shelbyville, Missouri – 17 January 1964, in Quincy, Illinois) was an American-Canadian mathematician, known for his pioneering work on linear inequalities. Education and career Dines received B.A. in 1906 and M.A. in 1907 from Northwestern University and Ph.D. in 1911 from the University of Chicago under Gilbert Bliss with thesis The highest common factor of a system of polynomial…

Key takeaways

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

Reference excerpt

Lloyd Lyne Dines (29 March 1885, in Shelbyville, Missouri – 17 January 1964, in Quincy, Illinois) was an American-Canadian mathematician, known for his pioneering work on linear inequalities.

Education and career Dines received B.A. in 1906 and M.A. in 1907 from Northwestern University and Ph.D. in 1911 from the University of Chicago under Gilbert Bliss with thesis The highest common factor of a system of polynomials in one variable, with an application to implicit functions. In 1911 he became an instructor of mathematics at Columbia University and then became an associate professor at the University of Arizona. From 1915 to 1934 he was a professor at the University of Saskatchewan. In 1928 he was elected to the Royal Society of Canada. In 1932 he was an invited speaker at the International Congress of Mathematicians in Zürich. From 1934 to 1945 he was a professor at the Carnegie Institute of Technology and chair of the mathematics department. After his retirement in 1945, Dines held visiting professorships at the University of Saskatchewan, Smith College, and Northwestern University.

Selected publications Dines, Lloyd L. (1913). "Concerning two recent theorems on implicit functions". Bull. Amer. Math. Soc. 19 (9): 462–467. doi:10.1090/s0002-9904-1913-02397-8. MR 1559394. Dines, L. L. (1915). "Complete existential theory of Sheffer's postulates for Boolean algebras". Bull. Amer. Math. Soc. 21 (4): 183–188. doi:10.1090/s0002-9904-1915-02595-4. MR 1559609. Dines, L. L. (1919). "Projective transformations in function space". Trans. Amer. Math. Soc. 20: 45–65. doi:10.1090/s0002-9947-1919-1501115-2. MR 1501115. Dines, L. L. (1924). "Concerning a suggested and discarded generalization of the Weierstrass factorization theorem". Bull. Amer. Math. Soc. 30 (5–6): 233–236. doi:10.1090/s0002-9904-1924-03889-0. MR 1560882. Dines, Lloyd L. (1924). "A theorem on the factorization of polynomials of a certain type". Trans. Amer. Math. Soc. 26: 17–24. doi:10.1090/s0002-9947-1924-1501262-7. MR 1501262. Dines, L. L. (1927). "Linear inequalities in general analysis". Bull. Amer. Math. Soc. 33 (6): 695–700. doi:10.1090/s0002-9904-1927-04461-5. MR 1561451. Dines, Lloyd L. (1927). "On sets of functions of a general variable". Trans. Amer. Math. Soc. 29 (2): 463–470. doi:10.1090/s0002-9947-1927-1501398-3. MR 1501398. Dines, L. L. (1928). "A theorem on orthogonal sequences". Trans. Amer. Math. Soc. 30 (2): 439–446. doi:10.1090/s0002-9947-1928-1501437-0. MR 1501437. Dines, Lloyd L. (1928). "A theorem on orthogonal functions with an application to integral inequalities". Trans. Amer. Math. Soc. 30 (2): 425–438. doi:10.1090/s0002-9947-1928-1501436-9. MR 1501436. Dines, L. L. (1930). "Linear inequalities and some related properties of functions". Bull. Amer. Math. Soc. 36 (6): 393–405. doi:10.1090/s0002-9904-1930-04956-3. MR 1561956. Dines, L. L. (1936). "Convex extension and linear inequalities". Bull. Amer. Math. Soc. 42 (6): 353–365. doi:10.1090/s0002-9904-1936-06299-3. MR 1563300. S2CID 44594799. with David Moskovitz: Moskovitz, David; Dines, L. L. (1940). "On the supporting-plane property of a convex body". Bull. Amer. Math. Soc. 46 (6): 482–489. doi:10.1090/s0002-9904-1940-07242-8. MR 0002008. Dines, Lloyd L. (1941). "On the mapping of quadratic forms". Bull. Amer. Math. Soc. 47 (6): 494–498. doi:10.1090/s0002-9904-1941-07494-x. MR 0004216. Dines, Lloyd L. (1942). "On the mapping of n quadratic forms". Bull. Amer. Math. Soc. 48 (6): 467–471. doi:10.1090/s0002-9904-1942-07707-x. MR 0006141. Dines, Lloyd L. (1943). "On linear combinations of quadratic forms". Bull. Amer. Math. Soc. 49 (6): 388–393. doi:10.1090/s0002-9904-1943-07925-6. MR 0008068. Dines, LL (November 1947). "On a theorem of von Neumann". Proc Natl Acad Sci U S A. 33 (11): 329–31. Bibcode:1947PNAS...33..329D. doi:10.1073/pnas.33.11.329. PMC 1079066. PMID 16588759.

References

Worked examples

Example 1 — a first encounter with Lloyd Dines

Start with the simplest possible case. Write down what Lloyd Dines 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 Lloyd Dines 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 Lloyd Dines 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 Lloyd Dines

In research: Lloyd Dines 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 Lloyd Dines 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: Lloyd Dines is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1885 births, 1964 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Lloyd Dines 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 Lloyd Dines in 20 minutes

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

Frequently asked questions

What is Lloyd Dines in simple terms?

Lloyd Lyne Dines (29 March 1885, in Shelbyville, Missouri – 17 January 1964, in Quincy, Illinois) was an American-Canadian mathematician, known for his pioneering work on linear inequalities. Education and career Dines received B.A. in 1906 and M.A. in 1907 from Northwestern University and Ph.D. in…

Why does Lloyd Dines 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 Lloyd Dines?

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 Lloyd Dines.