How did Cavalieri get his formula for the area underneath a parabola?

  • B
  • Thread starter erocored
  • Start date
  • #1
30
7
I know he had this ratio:
1604325468203.png

But how did he get this:
1604325593307.png
?
 

Answers and Replies

  • #3
35,052
6,791
I know he had this ratio:
View attachment 272042
But how did he get this:
View attachment 272043 ?
The result uses a formula for the sum of squares.
$$\sum_{k=1}^m k^2 = \frac{m(m + 1)(2m + 1)}6$$
Replace ##1^2 + 2^2 + \dots + m^2## in your first equation by the above, and you will get the result shown in the second equation.
 
  • Like
Likes Charles Link, Delta2 and erocored

Related Threads on How did Cavalieri get his formula for the area underneath a parabola?

Replies
7
Views
6K
Replies
1
Views
3K
Replies
8
Views
1K
Replies
7
Views
3K
Replies
4
Views
2K
Replies
1
Views
5K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
2
Views
9K
Top