astronomy

Jacob E. Goodman

Jacob E. Goodman 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 Jacob E. Goodman rather than just read about it. In short: Jacob Eli Goodman (November 15, 1933 – October 10, 2021) was an American geometer who spent most of his career at the City College of New York, where he was professor emeritus. Research Together, he and Richard M.

Key takeaways

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

Reference excerpt

Jacob Eli Goodman (November 15, 1933 – October 10, 2021) was an American geometer who spent most of his career at the City College of New York, where he was professor emeritus.

Research Together, he and Richard M. Pollack, his long-term collaborator, introduced concepts such as "allowable sequences of permutations" and "wiring diagrams", which have played an important role in discrete geometry, specifically in the study of arrangements of pseudolines and (more generally) oriented matroids. His work with Pollack includes such results as the first nontrivial bounds on the number of order types of polytopes, and a generalization of the Hadwiger transversal theorem to higher dimensions. He and Pollack were the founding editors of the journal Discrete & Computational Geometry. Goodman was the originator of the "pancake problem", an elementary question on permutations which he published under the pseudonym Harry Dweighter. The problem gave rise to the concept of pancake sorting. Goodman co-edited the book Handbook of Discrete and Computational Geometry with Joseph O'Rourke.

Music In 1999, Goodman returned to an old love, musical composition, and in 2002 was founding president of the New York Composers Circle.

Awards In 2012 he became a fellow of the American Mathematical Society.

Selected publications Dweighter, Harry; Garey, Michael R.; Johnson, David S.; Lin, Shen (1977), "Solutions of Elementary Problem E2569", American Mathematical Monthly, 84: 296, doi:10.2307/2318878, JSTOR 2318878. Goodman, Jacob E. (1980), "Proof of a conjecture of Burr, Grünbaum, and Sloane", Discrete Mathematics, 32: 27–35, doi:10.1016/0012-365x(80)90096-5. Goodman, Jacob E.; Pollack, Richard (1983), "Multidimensional sorting", SIAM Journal on Computing, 12 (3): 484–507, doi:10.1137/0212032. Goodman, Jacob E.; Pollack, Richard (1984), "Semispaces of configurations, cell complexes of arrangements", Journal of Combinatorial Theory, Series A, 37 (3): 257–293, doi:10.1016/0097-3165(84)90050-5. Goodman, Jacob E.; Pollack, Richard (1995), "Foundations of a theory of convexity on affine Grassmann manifolds", Mathematika, 42 (2): 305–328, doi:10.1112/s0025579300014613. Goodman, Jacob E.; Pollack, Richard; Sturmfels, Bernd (1990), "The intrinsic spread of a configuration in R^d", Journal of the American Mathematical Society, 3: 639–651, doi:10.1090/s0894-0347-1990-1046181-2 Cappell, Sylvain; Goodman, Jacob E.; Pach, János; Pollack, Richard; Sharir, Micha; Wenger, Rephael (1994), "Common tangents and common transversals", Advances in Mathematics, 106 (2): 198–215, doi:10.1006/aima.1994.1056. Goodman, Jacob E.; Pach, János; Pollack, Richard, eds. (2008), Surveys on Discrete and Computational Geometry: Twenty Years Later, Contemporary Mathematics, vol. 453, American Mathematical Society.

References

Worked examples

Example 1 — a first encounter with Jacob E. Goodman

Start with the simplest possible case. Write down what Jacob E. Goodman 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 Jacob E. Goodman 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 Jacob E. Goodman 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 Jacob E. Goodman

In research: Jacob E. Goodman 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 Jacob E. Goodman 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: Jacob E. Goodman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1933 births, 2021 deaths, City College of New York faculty, so understanding it makes those chapters shorter.
In everyday life: Look for Jacob E. Goodman 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 Jacob E. Goodman in 20 minutes

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

Frequently asked questions

What is Jacob E. Goodman in simple terms?

Jacob Eli Goodman (November 15, 1933 – October 10, 2021) was an American geometer who spent most of his career at the City College of New York, where he was professor emeritus. Research Together, he and Richard M.

Why does Jacob E. Goodman 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 Jacob E. Goodman?

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 Jacob E. Goodman.