How the Greeks Approached the Concept of Area. Archimedes' Method of Exhaustions

[@Helmutandmoshe]

Thank you so much for these lectures. I love your channel and I am so glad you are back and especially with this subject.

[@MathTheBeautiful]

Thank you, it means a lot!

[@AndresLara-hy3ip]

there seems to be a lot of cuts in this videos; do full versions exist? Outstanding teaching, by the way.

[@MathTheBeautiful]

Thank you! Unfortunately, full versions are not available, but none of the essential things are skipped in these tighter versions.

[@bobchannell3553]

At 2:16, could you take an average of the lengths of the two sides A and B, and make that the two sides of a square?

[@KaiseruSoze]

((a+b)/2)^2 = a*b? .... if a=3, and b = 4 then 12.25 = 12. Nope. You're thinking in terms of numbers rather than lines, squares and rectangles. You need to ask "what is the product of two different lines that equals the product of two equal lines.

[@bobchannell3553]

@@KaiseruSoze Thank you for your response. I can see that my attempt to solve this using numbers was wrong.

[@MathTheBeautiful]

So pleased to see substantive discussions under my videos!

[@alegian7934]

this might sound silly but... how do you draw a line perpendicular to a given point-on-a-line? i would try making a small circle at the given point, and then 2 bigger circles tangent to the small circle, and find their common cord... but that feels like too much work (?)

[@MathTheBeautiful]

Great question! Here's an answer: kzbin.info/www/bejne/bXzTZYNmm8-Ylc0

[@evankalis]

I notice that when you draw squares or matricies that the further away the edge of the square is, the bigger it gets. Its funny because of foreshortening it probably looks like a perfect circle to you when lecturing. Not a gripe but just something that makes me consider perspectives

[@MathTheBeautiful]

Yes, I've learned that you had to view the board head on for lines to come out straight.

[@theoremus]

In Latin, the word squaring is quadratura, i.e. Archimedes quadrature of the parabola.

[@abdurrahmanlabib916]

Thank you for these lectires! I think we audience would benefit a lot more if you could upload the full length lectures themselves.

[@MathTheBeautiful]

Thank you, I appreciate your kind words! Unfortunately, I'm not able to share the full lectures due to privacy considerations towards my students.

[@tanmaygupta6416]

what is name of the music? It is so satisfying

[@Helmutandmoshe]

That is Bach - Cello Suite No. 1 in G Major. Timeless and profoundly beautiful, just like mathematics.

[@MathTheBeautiful]

See kzbin.info/www/bejne/Z6HVqJiKbpqApZI

[@KaiseruSoze]

I love this... so far :)

[@MathTheBeautiful]

Thank you! It only gets better from here!

[@electric_sand]

I see it's going to be fun :)

[@MathTheBeautiful]

Indeed! Thank you!

[@majiddehbi9186]

so great

[@MathTheBeautiful]

Thank you!

[@Pluralist]