The Odd Number Law: How Galileo Cracked the Code of Motion

Galileo Galilei's inclined-plane experiment revealed Galileo's odd-number law of uniformly accelerated motion: in equal time intervals, a falling body's successive distances follow `1, 3, 5, 7`. The story moves from Aristotle's natural and forced motion to Philoponus and Buridan's impetus ideas, Galileo's water-clock measurements, the double-incline thought experiment, and the mathematical construction that combines uniform horizontal motion with vertical fall. #Galileo #Physics #HistoryOfScience #ScienceHistory #Mathematics #OddNumbers #Motion #ClassicalPhysics #ScienceEducation #MathAnimation WATCH MORE-- Video Video Cantor’s Nightmare: The Problem Math Can’t... CHAPTERS 0:00 Why Falling Objects Follow 1, 3, 5, 7 2:22 How Aristotle Explained Motion Before Galileo 8:03 Philoponus, Buridan, and the Missing Mover 10:34 How Galileo Measured Falling Motion With Water 11:51 The Square Law: Distance Grows With Time Squared 13:03 Why the Square Law Produces 1, 3, 5, 7 14:21 Galileo’s Double-Incline and the Idea of Inertia 17:34 Why Projectile Motion Forms a Parabola 22:14 Ideal Motion, Air Resistance, and Real Projectiles 23:34 Galileo’s Unsolved Collision Problem I use AI for narration to eliminate accent barriers. I hope that my research, script, and ideation will keep you coming back for more videos. This Video was made entirely using Manim - https://github.com/3b1b/manim Made possible by 3Blue1Brown - @3blue1brown and all the Manim Community members. SOURCES Galileo Galilei, *Dialogues Concerning Two New Sciences*, translated by Henry Crew and Alfonso de Salvio. Complete text digitized by the University of Virginia: https://galileoandeinstein.phys.virgi... Stanford Encyclopedia of Philosophy - Galileo Galilei: https://plato.stanford.edu/entries/ga... Stanford Encyclopedia of Philosophy - Aristotle's Natural Philosophy: https://plato.stanford.edu/entries/ar... Stanford Encyclopedia of Philosophy - Natural Philosophy in the Renaissance: https://plato.stanford.edu/entries/na... Stanford Encyclopedia of Philosophy - Plato's Middle Period Metaphysics and Epistemology: https://plato.stanford.edu/entries/pl... Plato, *Republic*, Book VII, 514a, Perseus Digital Library: https://www.perseus.tufts.edu/hopper/... Matteo Valleriani, *Tartaglia's Work on Theoretical Ballistics*, Edition Open Sources: https://edition-open-sources.org/sour... University of Oklahoma Libraries - On Conic Sections: https://galileo.ou.edu/exhibits/conic... Stephen M. Walley, *Aristotle, Projectiles and Guns*: https://arxiv.org/abs/1804.00716 Emil Wohlwill, *The Discovery of the Parabolic Shape of the Projectile Trajectory*: https://doi.org/10.1017/S026988970100... IMAGE CREDITS - • “Scratch circle (pseudotrace) on aragonite sand beach,” photograph by James St. John. Licensed under CC BY 2.0. Source: https://commons.wikimedia.org/wiki/Fi... Licence: https://creativecommons.org/licenses/... • “An Illustration of The Allegory of the Cave, from Plato’s Republic,” by 4edges. The unaltered image is included as one component of the video and remains licensed under CC BY-SA 4.0. Source: https://commons.wikimedia.org/wiki/Fi... Licence: https://creativecommons.org/licenses/... • “St Thomas Aquinas Kneeling and Offering His Works to the Roman Catholic Church,” fresco by Ludwig Seitz; photograph by Livioandronico2013. The unaltered photograph is included as one component of the video and remains licensed under CC BY-SA 4.0. Source: https://commons.wikimedia.org/wiki/Fi... Licence: https://creativecommons.org/licenses/... • “Ancient Lava on the Moon,” Artemis II image art002e012028, photographed by the Artemis II crew. Image background removed for the animation. Credit: NASA. Source: https://www.nasa.gov/image-detail/amf...