apr14a - MIT OpenCourseWare http://ocw.mit.edu 6.055J /...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 6.055J / 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 11 Bon voyage! 131 The second follow-up question is: Does the 3 occur in other problems and for the same reason? A related place is the volume of a sphere 4 3 V = r . 3 The ancient Greeks showed that the 3 in the 4 / 3 is the same 3 as in the pyramid volume. To explain their picture, Ill use method to find the area of a circle then use it to find the volume of a sphere. Divide a circle into many pie wedges. To find its area, cut somewhere on the circum- ference and unroll it into this shape: Each pie wedge is almost a triangle, so its area is bh / 2 , where the height h is approximately r . The sum of all the bases is the circumference 2 r , so A = 2 r r / 2 = r 2 . Now do the same procedure with a sphere: Divide it into small pieces that are almost pyramids, then unfold it. The unfolded sphere has a base area of pyramids, then unfold it....
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This note was uploaded on 02/24/2012 for the course MECHANICAL 6.055J taught by Professor Sanjoymahajan during the Spring '08 term at MIT.

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apr14a - MIT OpenCourseWare http://ocw.mit.edu 6.055J /...

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