The Ancient Mathematician Who Measured the Sun

In the 3rd century BC, Aristarchus of Samos found a method for calculating the relative sizes and distances of the sun, moon, and earth using some simple measurements and...triangles.

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Special thank you to Alex Kontorovich for working with me on this video! This video is loosely based on his Princeton University lecture about Aristarchus: https://youtu.be/VdeyI8KMqts?si=WSEr15AfL-CUS-z5
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Written by Ben Syversen and Alex Kontorovich
Produced, edited, and animated by Ben Syversen
Aristarchus and Archimedes Illustrations: Kendall Eddy
Additional editing: Sara Adelberg
Additional animation: Pranav Kumar
Camera: Giacomo Belletti
Thumbnail design: Mostafa Hasan

Music: Epidemic Sound

Additional thank you to Viktor Blåsjö for speaking with me about this topic.
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Chapters:
00:00 - Intro
01:03 - 1) The Half Moon
04:41 - 2) The Solar Eclipse
07:24 - 3) The Dime Experiment
09:00 - 4) The Lunar Eclipse
13:24 - Heliocentrism
16:10 - Eratosthenes
18:19 - Copernicus
19:45 - The Universe
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Works consulted for this video:

•Aristarchus of Samos, The Ancient Copernicus - translated and annotated by Thomas Heath - https://archive.org/details/aristarchusofsam00heatuoft/page/n5/mode/2up

•Aristarchus’s On the Sizes and Distances of the Sun and the Moon: Greek and Arabic Texts - Berggren and Sidoli - http://individual.utoronto.ca/acephalous/Berggren_Sidoli_2007.pdf

•Archimedes - The Sand Reckoner - https://web.calstatela.edu/faculty/hmendel/Ancient%20Mathematics/Archimedes/SandReckoner/Ch.1/Ch1.html

•Viktor Blåsjö - podcast - Opinionated History of Mathematics - Heliocentrism in Antiquity - https://open.spotify.com/episode/6q80OeT8x1apeZr6JC9EKi?si=239fa7115d944f3b
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To learn more about Aristarchus:

•3Blue1Brown: Terence Tao on how we measure the cosmos | The Distance Ladder Part 1 - https://youtu.be/YdOXS_9_P4U?si=T4FpcsQVtoViKilj

•https://terrytao.wordpress.com/2025/02/13/cosmic-distance-ladder-video-with-grant-sanderson-3blue1brown-commentary-and-corrections/
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Images:

Images are public domain via Wikimedia and Metropolitan Museum of Art
Additional images licensed via Envato Elements
Image of the “well” in Syene created in Midjourney

Stellar parallax diagram - ESA/ATG medialab - https://www.esa.int/Science_Exploration/Space_Science/Gaia/Parallax