Archimedes derives the volume of a sphere formula

Gary Rubinstein teaches how Archimedes
in 'The Method,' a manuscript which was lost between 900 AD and 1900 AD (and then lost again until 1998) first derived the formula for the volume of a sphere using the law of the lever.

Category:

Education

Tags:

• Screencast-O-Matic.com

[nymathteacher]

@no181c If you create triangle AOC it will be a right triangle, and altitude OS is drawn to hypotenuse AC. There is a theorem that says that altitude drawn to hypotenuse is mean proportional to two parts of the hypotenuse. Also could do it by seeing that triangle AOC is similar to triangle ASO and triangle SCO. Because ASO is similar to OSC, you could also get SO/AS=SC/SO which becomes AS*SC=SO^2.  Third way by Mathew2400.

[Matthew2400]

@no181c There is a rule in circles where if you draw any two lines inside a circle that cross each other, then the product of the two parts of one line will equal the product of the two parts of the other line. Since SO was exactly halfway across the intersection, then multiplying SO by SO gives SO squared. For example: if you had a line that was 10cm long intersecting a line that was 26cm long, then multiplying the two parts of the 10cm line (5 * 5) gives the 26cm line product (25 * 1).

[no181c]

Lost at "AS times SC equals to SO squared" (4:10) - How is this derived?

[davidvwilliamson]

I don't understand how to put a link in here I'll try breaking it up with underscores h_t_t_p_:_/_/_ durealeyes._c_o_m_/_quad9c_.h_­t_m_l

[eggsontheside]

Is SO^2 supposed to be (SO)^2 ?



[360kal]

is your sir name is actually Rubinstein that's so cool

[ctk06]

:D You're so awesome, Mr.Rubinstein.

[clixsyt]

Dude thanks for the upload. Its really clever the way this all works out.