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mathwonk

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wow, just opened archimedes and found precisely the statements i have been making to people lately about circles and spheres:

namely he says exactly that (for the pruposes of computing area) a circle is a triangle whose vertex is at the center and whose height is the radius. and (in regard to volume) a sphere is a cone whose vertex is at the center and height is the radius.

it makes me fel very good to have arrived at exactly the perspective of archimedes in these matters, although 2,000 years later, and with a great deal of instruction.

too bad i did not read him as a child, i would have known this 50 years ago.

oh, and archimedes knew the location of the centroid both of a triangle and of a cone, the latter something i just learned a few weeks ago and taught to my class.

and euler computes the values of zeta at even integers, i.e. the sum of the reciprocal powers 1/n^2k, for k up to 13, in his precalculus book, vol 1, page 139. actually he just states them, implying the computations are straighforward.

i have still not arrived at euler's perspective.

namely he says exactly that (for the pruposes of computing area) a circle is a triangle whose vertex is at the center and whose height is the radius. and (in regard to volume) a sphere is a cone whose vertex is at the center and height is the radius.

it makes me fel very good to have arrived at exactly the perspective of archimedes in these matters, although 2,000 years later, and with a great deal of instruction.

too bad i did not read him as a child, i would have known this 50 years ago.

oh, and archimedes knew the location of the centroid both of a triangle and of a cone, the latter something i just learned a few weeks ago and taught to my class.

and euler computes the values of zeta at even integers, i.e. the sum of the reciprocal powers 1/n^2k, for k up to 13, in his precalculus book, vol 1, page 139. actually he just states them, implying the computations are straighforward.

i have still not arrived at euler's perspective.

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