FC2Video

命) x^2+1は2つの平方数の和で表わせる(真) ■証明(?) 1=1^2 より x^2+1 =x^2+1^2 ■判定方法 「2つの平方数の和」の表現は複数存在する場合がある 表現が複数の場合は合成数 x^2+1^2のみの場合は素数 ただし、x^2+1が(2)以外の偶数の場合は合成数 偶数の場合、合成数なのに表現がx^+1^2のみと判定される場合がある_ x^2+1の約数と「2つの平方数の和」が関係しているため判定できる 表現の個数は素因子の個数とは関係していない 同じ素因子複数で構成(素因子のｎ乗）されている場合、表現の個数が減ってしまう 素因数分解や素因子を考えなくても判定できる たぶん… 2025/5/1 「二つの平方数の和」による素数判定法について ある数が二つまたはそれ以上の異なる方法によって二つの平方数に分割しうるとき, それは素数でなく, 二つ以上の因子の合成である. (L. Euler, 1749) https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://yu200489144.hatenablog.com/entry/2021/07/08/213334&ved=2ahUKEwiTm_GtwoKNAxWbk1YBHc_hNewQFnoECCIQAQ&usg=AOvVaw1wwifGba4KK0mk3qGMwOOK

Rhein Main Gedanken 134

'e' (Euler's Number) - Numberphile

Dancer: Ashlynn Marie Lyrics: AKIRA☆SKYHIGH/Isaac Asimov Music: AKIRA☆SKYHIGH ROBOT! A robot may not injure a human being, or, through inaction, allow a human being to come to harm. android artificial intelligence computer vision standard robot language I'm a ROBOT ROBOT ROBOT ROBOT TECHNO TECHNO TECHNO TECHNO A robot must obey the orders given it by human beings except where such orders would conflict with the First Law. vision sensor acoustic sensor ultrared sensor ultrasonic sensor I'm a ROBOT ROBOT ROBOT ROBOT TECHNO TECHNO TECHNO TECHNO A robot must protect its own existence as long as such protection does not conflict with the First or Second Law Newton equation Euler equation Lagrangian formulation Coriolis acceleration I'm a ROBOT ROBOT ROBOT ROBOT TECHNO TECHNO TECHNO TECHNO ROBOT ROBOT ROBOT ROBOT TECHNO TECHNO TECHNO TECHNO A robot may not injure a human being

Lyrics: AKIRA☆SKYHIGH/Isaac Asimov Music: AKIRA☆SKYHIGH ROBOT! A robot may not injure a human being, or, through inaction, allow a human being to come to harm. android artificial intelligence computer vision standard robot language I'm a ROBOT ROBOT ROBOT ROBOT TECHNO TECHNO TECHNO TECHNO A robot must obey the orders given it by human beings except where such orders would conflict with the First Law. vision sensor acoustic sensor ultrared sensor ultrasonic sensor I'm a ROBOT ROBOT ROBOT ROBOT TECHNO TECHNO TECHNO TECHNO A robot must protect its own existence as long as such protection does not conflict with the First or Second Law Newton equation Euler equation Lagrangian formulation Coriolis acceleration I'm a ROBOT ROBOT ROBOT ROBOT TECHNO TECHNO TECHNO TECHNO ROBOT ROBOT ROBOT ROBOT TECHNO TECHNO TECHNO TECHNO A robot may not injure a human being

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Four-part series about the history of mathematics, presented by Oxford professor Marcus du Sautoy. By the 17th century, Europe had taken over from the Middle East as the world's powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was now on to discover the mathematics to describe objects in motion. In this programme, Marcus du Sautoy explores the work of René Descartes and Pierre Fermat, whose famous Last Theorem would puzzle mathematicians for more than 350 years. He also examines Isaac Newton's development of the calculus, and goes in search of Leonard Euler, the father of topology or 'bendy geometry' and Carl Friedrich Gauss, who, at the age of 24, was responsible for inventing a new way of handling equations: modular arithmetic.

A simple physics simulation (lines represent springs with masses at the vertices constrained to move vertically) uses the Euler method to approximate positions, which, clearly has cool effects. The springs are damped and I don't touch them after the initial flick, but, well...

Matlab video to demonstrate Euler's equation in action. From Bob Hay.