Talk:Method of exhaustion

From Wikipedia, the free encyclopedia

WikiProject Mathematics
Mathematics Portal
This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating: Start Class Mid Priority  Field: Geometry
Please update this rating as the article progresses, or if the rating is inaccurate. Please also add comments to suggest improvements to the article.


[edit] area in a spiral

"The area bounded by one spiral rotation and a line is 1/3 that of the circle having a radius equal to the line segment length" - doesn't this depend on the type of spiral? —Preceding unsigned comment added by 193.172.19.20 (talk) 18:36, 28 November 2007 (UTC)

[edit] Area/Volume Descriptions

" * The area bounded by the intersection of a line and a parabola is 4/3 that of the triangle having the same base and height;

   * The area of an ellipse is proportional to a rectangle having sides equal to its major and minor axes;
   * The volume of a sphere is 4 times that of a cone having a base and height of the same radius;
   * The volume of a cylinder having a height equal to its diameter is 3/2 that of a sphere having the same diameter;
   * The area bounded by one spiral rotation and a line is 1/3 that of the circle having a radius equal to the line segment length;
   * Use of the method of exhaustion also led to the successful evaluation of a geometric series (for the first time)."


There needs to be images associated with these area/volume formulas. Also, the volume of a cone compared to a sphere is not exactly clearly stated.

Vol_sphere=4 * Vol_cone, if b=h=r A beginner would likely assume that the radius of the base of the cone, and the height are the same, but still wouldn't be sure this was correct? This could be a lot clearer with a diagram... Are there any already on the site? —Preceding unsigned comment added by JWhiteheadcc (talk • contribs) 02:36, 17 December 2007 (UTC)