[過去ﾛｸﾞ] ガロア第一論文と乗数イデアル他関連資料スレ13 (1002ﾚｽ)

ガロア第一論文と乗数イデアル他関連資料スレ13 http://rio2016.5ch.net/test/read.cgi/math/1738367013/

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722: 現代数学の系譜 雑談 ◆yH25M02vWFhP [] 2025/02/11(火) 19:45:53.55 ID:zr+dFWV7 つづき https://en.wikipedia.org/wiki/Proofthat%CF%80isirrational Proof that π is irrational In the 1760s, Johann Heinrich Lambert was the first to prove that the number π is irrational, meaning it cannot be expressed as a fraction a/b, where a and b are both integers. In the 19th century, Charles Hermite found a proof that requires no prerequisite knowledge beyond basic calculus. Three simplifications of Hermite's proof are due to Mary Cartwright, Ivan Niven, and Nicolas Bourbaki. Another proof, which is a simplification of Lambert's proof, is due to Miklós Laczkovich. Many of these are proofs by contradiction. In 1882, Ferdinand von Lindemann proved that π is not just irrational, but transcendental as well.[1] Lambert's proof 略 Hermite's proof 略 Cartwright's proof 略 Niven's proof 略 Bourbaki's proof 略 Laczkovich's proof 略 以上 http://rio2016.5ch.net/test/read.cgi/math/1738367013/722

723: １３２人目の素数さん [] 2025/02/11(火) 19:48:42.26 ID:MW1+hP7T >>721-722　数学のスの字もわからん馬鹿素人は口をはさむなｗ 肝心なことは全部略のくせにｗｗｗ http://rio2016.5ch.net/test/read.cgi/math/1738367013/723

736: 現代数学の系譜 雑談 ◆yH25M02vWFhP [] 2025/02/11(火) 23:27:40.41 ID:zr+dFWV7 >>724 > https://manabitimes.jp/math/2697 ご苦労さまです それ >>722 https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational Proof that π is irrational にあるよ Niven, Ivan (1947)だね Niven's proof This proof uses the characterization of π as the smallest positive zero of the sine function.[9] Suppose that π is rational, i.e. π=a/b for some integers a and b which may be taken without loss of generality to both be positive. Given any positive integer n, we define the polynomial function: f(x)=x^{n}(a-bx)^{n}/{n!} and, for each x∈R let F(x)=f(x)-f''(x)+f^4(x)+・・・ +(-1)^nf^2n(x). Claim 1: F(0)+F(π)} is an integer. 以下略す References 9. Niven, Ivan (1947), "A simple proof that π is irrational" (PDF), Bulletin of the American Mathematical Society, vol. 53, no. 6, p. 509, doi:10.1090/s0002-9904-1947-08821-2 http://rio2016.5ch.net/test/read.cgi/math/1738367013/736

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