The Challenge of π or How Archimedes Squared the Circle. Introduction to Differential Geometry

Complete playlist: • The MOST Fundamental C...
grinfeld.org
/ pavelgrinfeld
grinfeld.org/books/An-Introdu...
grinfeld.org/books/A-Tensor-D...

[@tomholroyd7519]

The beauty of mathematics: working with quantities you don't understand, like Planck's constant. Planck didn't understand what it meant at first, it was just an algebraic trick. But it turned out to redefine our understanding of the universe. Mathematical theorems can do that.

[@SamHuttonTV]

good to see you back, Pavel

[@MathTheBeautiful]

Thank you!

[@punditgi]

Excellent video 🎉😊

[@MathTheBeautiful]

Thank you!

[@YommiOfficial]

Always enjoy these

[@MathTheBeautiful]

Thank you, I'm glad to hear it!

[@SongSeeker7]

Trying to square the circle I came across this discovery. If I draw 3 circles of radius r in a ring, then the center deltoid I calculated to be [root(3) - pi/2]r*r Using 1 circle and 2 deltoids pi is completely eliminated and I get a catface shape that has area 2*root(3)*r*r . I can completely fill a 2D space with these shapes.

[@KaiseruSoze]

Great derivation - no dx's yaaay. (or dr's)

[@MathTheBeautiful]

Yeah!

[@theoremus]

@@MathTheBeautiful I like this approach also.

[@theoremus]

Hence, Archimedes was working with a Limit even though he did not have a formal definition of the Limit.

[@MathTheBeautiful]

Yes, as did Newton, Leibniz, Euler.

[@phscience797]

@@MathTheBeautiful I think what Newton, Leibniz and Euler did was much more egregious (though it was in retrospect the right thing to do). Archimedes still provided his formal proof, cleverly avoiding invoking the infinite, which these later people did little of (at least as it relates to computing properties of curves).

[@Pluralist]

[@rickperez8975]

4:03 😂😂😂

[@MathTheBeautiful]

My students deserve better!