1
vote
0answers
405 views

Area Under Generalized Parabolas and Hyperbolas without Calculus.

This is shorter and more specific version of certain questions about a rather simple quadrature method. The answers I got were great but not what I asked. The terms in the title for $y=x^p$ look ...
9
votes
4answers
868 views

Integrating Powers without much Calculus

I'll jump into the question and then back off into qualifications and context Using the definition of a definite integral as the limit of Riemann sums, what is the best way (or the very good ways) ...
3
votes
0answers
418 views

sine and Archimedes' derivation of the area of the circle

The elementary "opposite over hypotenuse" definition of the sine function defines the sine of an angle, not a real number. As discussed in the article "A Circular Argument" [Fred Richman, The College ...
22
votes
1answer
2k views

Why do we use $\epsilon$ and $\delta$?

My understanding (from a talk by Rob Bradley) is that Cauchy is responsible for the now-standard $\epsilon{-}\delta$ formulation of calculus, introduced in his 1821 Cours d’analyse. Although perhaps ...
15
votes
3answers
5k views

How did Bernoulli prove L'Hôpital's rule?

To prove L'Hôpital's rule, the standard method is to use use Cauchy's Mean Value Theorem (and note that once you have Cauchy's MVT, you don't need an $\epsilon$-$\delta$ definition of limit to ...
11
votes
1answer
721 views

What is happening to Martin Gardner's files?

Martin Gardner kept voluminous correspondence with amateur and professional mathematicians worldwide throughout his career. His files are a treasure trove of information about all areas of ...
3
votes
1answer
425 views

What are the oldest illustrations of “Venn” diagrams?

Graphical representations of intersection of sets as logical combinations are much older than Venn. Euler and Leibniz are often quoted and the current Wikipedia article also quotes Ramon Llull but I ...