Johann Bernoulli (= Jean; 1667–1748) posed the problem of finding the ‘brachistochrone’: the curve between two points along which a body starting from rest at the higher point and freely accelerated by uniform gravity would descend in minimum time to the lower.

Gottfried Wilhelm Leibniz (1646–1716) thought the problem beautiful; so did Guillaume de l’Hospital (1661–1704).

Bernoulli (and others) proved that the brachistochrone was again an inverted cycloid. He thought that the equality of the cycloid, tautochrone, and brachistochrone curve would leave his readers ‘petrified with astonishment’, and thought that it suggested some deep design in nature.

One of Bernoulli's proofs was what he considered a ‘very beautiful’ geometric demonstration that the cycloid was the brachistochrone.

But he did not publish it until 20 years later. Why? Apparently in part due to Leibniz, who had thought it so beautiful and extraordinary that he counselled against publication, with the aim of ‘so frustrating those who are not very grateful and who are accustomed to profiting from the inventions of others’.

**Here, mathematical beauty contributed to the suppression, albeit temporary, of mathematical knowledge.**

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#Bernoulli #JohannBernoulli #JeanBernoulli #brachistochrone #Leibniz

Interestingly, it is also the curve that solves the #Brachistochrone problem, which means that starting at a cusp on the inverted curve (maximum height), a frictionless ball will roll under uniform gravity in minimum time from the start to any other point on the curve, even beating the straight line path.

#Mathematics #Geometry #Maths #AppliedMathematics #Mechanics #Kinematics #Dynamics #Physics

Ep 108 - Cette acnée là

Saison 3️⃣ Épisode 4️⃣ du podcast Les Amis Causent !🎤 Toujours enregistré depuis La Cordée (https://www.la-cordee.net/) à Lyon avec Diane, Corentin, Jean-Baptiste, Pierre-Michel et Clément !😂 Dans cet épisode les amis causent de passage entre deux rues et de passage entre la vie et la mort, de virevoltant américain, de vol en vol, de défis australiens, de fêtes païennes, de toboggan et de la bonne année. Et tout ça dans nos différentes rubriques : les infos insolites, le plan Culture, le jeu et la découverte musicale. Bonne écoute !🙈 Attention spoiler ! Ne lisez pas le contenu ci-dessous tant que vous n'avez pas écouté l'épisode !📰 Les infos insolites de PM :Voici la rue la plus étroite au monde, elle ne mesure que 29 cm de large et se trouve en France (https://www.ouest-france.fr/provence-alpes-cote-dazur/gassin-83580/voici-la-rue-la-plus-etroite-au-monde-elle-ne-mesure-que-29-cm-de-large-et-se-trouve-en-france-1e645694-8eaa-11ee-b244-826800b6b4f5)A car-sized tumbleweed made quite a scene on a California highway (https://www.npr.org/2023/11/24/1214974578/giant-tumbleweed-california)Ce Breton est champion de France d’éloquence... de cérémonies de pompes funèbres (https://www.ouest-france.fr/bretagne/morbihan/brieuc-employe-de-pompes-funebres-a-auray-est-champion-de-france-deloquence-0cd09b4a-92ce-11ee-8602-1e868188f4e2)Lost tomato found aboard International Space Station after eight months (https://www.upi.com/Odd_News/2023/12/08/International-Space-Station-lost-tomato-found-Frank-Rubio/4161702071512/)Australian men visit 99 pubs in 24 hours to break world record (https://www.upi.com/Odd_News/2023/12/05/australia-Guinness-World-Records-pub-crawl/1441701809097/)🧠 Le plan Culture de JB :Walpurgisnacht (https://fr.wikipedia.org/wiki/Nuit_de_Walpurgis)Brachistochrone (https://fr.wiktionary.org/wiki/brachystochrone)🕹️ Le jeu de PM :Retrouve l'année correspondant au son🎧 La découverte musicale de Clément :Naudin - La seule fenêtre (https://www.youtube.com/watch?v=jKl1kaZ-kAI)

Ep 108 - Cette acnée là | Les Amis Causent