Torricelli's Trumpet Proof using Method of Indivisibles

  • Context: Graduate 
  • Thread starter Thread starter BlackTiger
  • Start date Start date
  • Tags Tags
    Method Proof
Click For Summary
SUMMARY

The discussion focuses on proving Torricelli's trumpet, which describes a solid of revolution with finite volume but infinite surface area, specifically for the function y=1/x about the x-axis for x ≥ 1. The user seeks assistance in understanding this proof using the method of indivisibles, avoiding modern integral notation. Historical context and references to original works are also mentioned, highlighting the scarcity of resources that explain Torricelli's original methods.

PREREQUISITES
  • Understanding of Torricelli's trumpet concept
  • Familiarity with the method of indivisibles
  • Basic knowledge of geometric solids of revolution
  • Historical context of calculus development
NEXT STEPS
  • Research the historical methods used by Torricelli in his proofs
  • Study the method of indivisibles in detail
  • Explore geometric interpretations of solids of revolution
  • Read original texts or translations related to Torricelli's work
USEFUL FOR

Mathematicians, historians of mathematics, and students interested in classical calculus methods and the development of mathematical concepts.

BlackTiger
Messages
2
Reaction score
0
Hey am currently struggling with the proof for Torricelli's trumpet (finite volume with infinite surface area for function y=1/x about the x-axis for x > or = to 1) without using the modern notation, i.e., integrals. Any help would be appreciated...

i have found a couple of explanations for using the method of indivisibles but they seem to be few and far between with a lot of it being very very basic and not really giving an understanding of how torricelli himself worked it out before then proving it using integrals in the modern day way so i am looking for any help, be it website links or your own knowledge to point me in the right direction for figuring this all out

many thanks
 
Physics news on Phys.org

Similar threads

Graduate How do I apply the method of steepest descents to this integral?
  • · Replies 1 ·
Replies
1
Views
3K
High School Question about change of variables
  • · Replies 29 ·
Replies
29
Views
5K
Undergrad Explanation and clarifications in epsilon-delta limit proofs
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Question about proof of Great Picard Theorem
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Integral equations -- Picard method of succesive approximation
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Unclear step in "Change of variable in a multiple integral" proof
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Trying an alternate Proof of the Fundamental Theorem
  • · Replies 11 ·
Replies
11
Views
3K
MHB Finding Approximate Critical Number with Newton's Method
  • · Replies 7 ·
Replies
7
Views
5K
Graduate Finite area with infinite volume
  • · Replies 2 ·
Replies
2
Views
6K
Graduate Summing over continuum and uncountable numerocities
  • · Replies 1 ·
Replies
1
Views
3K