Pi = 3.1415 Proof: Archimedes' Geometric Proof

in MES Science11 months ago (edited)

In this video I go through one of the oldest Pi derivations known to man. Archimedes proved that Pi is equal to roughly 3.141 over 2000 years ago using basic geometry. He took a regular hexagon (6-sided polygon with equal sides) and inscribed it inside a circle of radius 1 and another regular hexagon outside the circle. He would double the length of the polygons until the perimeter of the polygon was roughly that of the circle and from there, he would calculate Pi. He stopped at a 96-sided polygon but I go further with Microsoft Excel up to around a 100,000 sided polygon.

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Pi = 3.1415… Proof

Archimedes Pi Proof.png

Archimedes’ Proof

  • Archimedes of Syracuse (c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer.
  • Calculated Pi using basic geometry in a recursive manner
    • Calculated perimeter of a regular hexagon (6-sided polygon) inscribed inside and outside a circle using Pythagoras.
    • Doubled the sides until you was satisfied with a 96-side polygon










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That is an important concept! Thanks for teaching it

You remind me of my school years and fill me with sweet melancholy! I would never have believed that I would say that! Haha! Very good work and analysis!