question 33rd and angles in daily life and the new Yorker
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The Rockmore theorem made its first—and perhaps only—named appearance in print in 1977, in the journal Physics Letters, Volume 72B, No. 4. A photocopy of the journal page hung on my father’s office door, at Rutgers University, in New Jersey. The author of the article—one B. L. Birbrair, of the Academy of Sciences of the U.S.S.R.—wrote that, in 1959, my dad had demonstrated that the “interaction between quasiparticles exactly compensates” for “the difference between the effective and real mass” of an “infinite non-superfluid fermi system.” Since then, he went on, “the statement J(Δ = 0) = Jrig” has been known as “the Rockmore theorem.”
My dad had underlined those last three words in bold, black pen. Other professors on the same hallway displayed conference posters on their doors, in which they were featured as keynote speakers in exotic locales. My dad couldn’t produce such a poster, but the photocopy, which hung amid New Yorker cartoons, preprints, and departmental announcements, showed something arguably more valuable.
Theorems are mathematical facts justified by proofs—logical, airtight arguments made of other facts and deductions. Usually, a proof consists of statements taking the form “if this, then that”; this chain of “ifs” is grounded in bedrock mathematical truths. In high-school geometry, you probably saw some simple proofs—two-column accounting ledgers, with statements on one side and justifications on the other. Many proofs by professional mathematicians are baroque in comparison; they contain twists, turns, and surprise appearances, with intermediate steps, known as propositions, claims, or “lemmas,” that require proofs of their own. A theorem is only published if it’s been deemed interesting by journal editors and successfully “refereed” by external evaluators. Mathematicians prove thousands each year, but of the many published theorems only a few are named.
The eponymous theorems are the most famous, but are they rightly named? There’s Pythagoras’ well-known beauty, a fact about the three sides of a right triangle: the sum of the squared lengths of its two shorter sides equals the squared length of its hypotenuse (a2 + b2 = c2). A proof for the Pythagorean Theorem can be found among Euclid’s “Elements,” the thirteen-volume treatise on geometry that many see as an exemplar of Greek mathematics. The Roman statesman and philosopher Cicero connected the theorem to Pythagoras some five centuries after his death, though the attribution is hardly a slam dunk. Part of the beauty of Pythagoras’ theorem is that it admits revelation through a broad range of proofs. So far, there have been more than a hundred. Even Albert Einstein set one down. It seems likely that some other early geometer could have been the first.
Answer:
Doraemon is a Japanese manga series written and illustrated by Fujiko F. Fujio. The manga was first serialized in December 1969, with its 1,345 individual chapters compiled into 45 tankōbon volumes, published by Shogakukan from 1970 to 1996.