explore | Grilled Cheese

Haha ou l'éclair de la compréhension mathématique
Martin Gardner

En mathématiques aussi, " toujours l'inattendu arrive ".
La solution d'un problème, souvent surprenante, est le fruit du " Haha ", cet éclair de la compréhension inventive, si différente d'une plate compilation effectuée par ordinateur.
Martin Gardner pénètre dans la pensée du mathématicien pour nous faire vivre cette illumination. Une telle démarche est utile pour la santé de notre cerveau : nous pouvons, à la différence de la machine, apprendre à être inventif.

cf eureka

$Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Archimedes’ Equiareal Map Theorem : Let S be the unit sphere defined relative to the x, y and z axes by x^2 + y^2 + z^2 = 1 and let S′ be the bounding cylinder defined by x^2 + y^2 = 1. Let f be the map f : (x, y, z) → (x / √(x^2 + y^2) , y / √(x^2 + y^2) , z) from S \{(0, 0, 1), (0, 0, −1)} to S ′ which takes a point P on the sphere having height zP, |zP| < 1, to the nearest point on the cylinder which has height zP and which is collinear with P and (0, 0, zP). Then f is an equiareal diffeomorphism.$

Raise Good Ruckus story graphic showing mathematician Eric Harshbarger standing beside several enormous wooden many-sided dice at Auburn University. The dice are covered with large numbered faces. Headline: “Mathematicians Solved ‘Who Goes First?’” Text explains that five specially numbered 60-sided dice let five players roll once, avoid ties and keep everyone’s odds fair.