Math Mysteries: Proving Volume Equality

[dracobook]

The first is how did he figure out that the volume of a cone and a sphere is equal to that of a cylinder?

How do you prove that some infinite series are larger than others?

What does : and the verticle dash mean again?

 

[NewScientist]

research yourself

 

[HallsofIvy]

The first is how did he figure out that the volume of a cone and a sphere is equal to that of a cylinder?

How do you prove that some infinite series are larger than others?

What does : and the verticle dash mean again?

1. How did who figure it out? Archimedes?

2. I don't- I don't even know how to compare the size of series. Do you mean that the sum of some infinite series is larger than the sum of others?

3. The vertical dash may have many meanings depending on the context.
(Odd, I don't remember having told you that before.)

 

[Werg22]

In order to understand the awnser to those quesions dracobook you'll need precalculus and calculus. Exept I really ignore how the Greeks calculated the volume and area of a sphere without calculus.

 

[arildno]

As to 1., if I remember correctly, Archimedes made a clever "balancing argument" for this in his work "The Method"(?).