I blurted:
A diagram purporting to explain solar eclipses has two mysterious lines, apparently delimiting the penumbra, tangent to the sun, moon, and Earth! Even in the zero probability event that the three would align perfectly, this is wrong by a factor of 3,
referring to the tangent of half the angle between the lines. But it's closer to 1.8. Actually, its reciprocal.
and falsely implies that there is never a time when the whole sunlit hemisphere can see an at-least-partial eclipse.
This is backwards. The bogus lines show the penumbra all but covering one hemisphere. But the taper of the umbra from the lunar limb to essentially zero at the Earth is only slightly more gradual than the taper of the penumbra from the Earth back to the limb, which makes for a shadow slightly wider than twice the moon. rshad dmoon rsun dmoon dmoon rsun ----- = ---------- + ----- + 1 ~ 2.03 ~ ---------- + 1 rmoon dsun rmoon dsun dsun rmoon r:=radius, d:=distance from Earth. Picture: http://sunearth.gsfc.nasa.gov/eclipse/SEplot/SEplot2001/SE2006Mar29T.gif Sorry for the confission. --rwg PS, this lets me squeeze in one more math howler: "Find the area of a circle of radius 30cm. Round to the nearest tenth. Use pi = 3.14 ." It may not have been exactly 30, but they wanted five significant figures from a three digit value of pi! I forgot to ask if kids who used better values of pi got marked off.
"The weak force is the key to the power of the Sun."
I guess they don't want kids to know that solar power is really nuclear. PPS: I seem to have slipped that eclipse booboo past inventor/telescope maker Alan Adler, who recently remarked of the burgeoning field of cosmology: "Never have so many known so little about so much". I guess he never met the editorial board of Prentice Hall Science. Finally, apropos astronomy quotes is Rich's inspirational "'Tis better to shoot out a single street lamp than to curse the light pollution."
--- "R. William Gosper" <rwg@spnet.com> wrote:
"The weak force is the key to the power of the Sun."
I guess they don't want kids to know that solar power is really nuclear.
That statement about the weak force has a bit of truth to it, since without the weak force, protons could not be converted into the neutrons needed to make helium. But then I'm approaching the book from the point of view of someone who understands nuclear physics, not that of the poor student. When you quoted that sentence from the book, my first guess was that the author was a simple ignoramus, and I still think that's the case. He could have said that nuclear fusion powers the sun. Fusion is still politically correct, and will be up to the moment the generators are built. Then it will be demonized; tritium playing the current role of plutonium. The MIT Open Course Ware ( http://ocw.mit.edu/index.html ) looks like it will develop into a wonderful resource when, as they promise, all the courses will be online. There are also wonderful resources hidden away in books; the problem is identifying the few good ones among all the trash. Something we could do to help the bright students stuck in lousy schools is to prepare reading lists of good books and post them on the internet. The lists should include politically incorrect material, not only because much that is scientifically correct is politically incorrect, but also because then the schools might then try to have the lists banned, and that would generate publicity that no amount of money could buy. Gene __________________________________ Do you Yahoo!? The New Yahoo! Search - Faster. Easier. Bingo. http://search.yahoo.com
On Saturday, May 10, 2003, at 13:36 America/Denver, R. William Gosper wrote:
PS, this lets me squeeze in one more math howler: "Find the area of a circle of radius 30cm. Round to the nearest tenth. Use pi = 3.14 ." It may not have been exactly 30, but they wanted five significant figures from a three digit value of pi! I forgot to ask if kids who used better values of pi got marked off.
Mention of a circle of thirty something-or-others reminded me of the famous passage in II Chronicles 4:2 (also 1 Kings 7:23 (KJV)): 4:2 Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about. Ergo pi = 3. But at least he has D = 2*R right. It is probably urban legend that bills have been introduced in one or another benighted state legislature to insure that pi is taught to be three to the kiddies thereof (one of the Benighted States of America? where all wheels are hexagonal).
On 11 May 2003 at 9:12, Roland Silver wrote:
It is probably urban legend that bills have been introduced in one or another benighted state legislature to insure that pi is taught to be three to the kiddies thereof (one of the Benighted States of America? where all wheels are hexagonal).
This from a posting to sci.math by Allan Adler in 1991: ======================================================== "House Bill No. 246, Indiana State Legislature, 1897", [...] The author of the bill was Edwin J. Goodwin, M.D. It was introduced into the House by Mr. Taylor I. Record, Representative from Posey County, on Jan.18, 1897. The following is the statement of the bill: "HOUSE BILL NO. 246 "A bill for an act introducinga new mathematical truth and offered as a contribution to education to be used only by the State of Indiana free of cost by paying any royalties whatever on the same, provided it is accepted and adopted by the official action of the legislature of 1897. "Section 1. Be it enacted by the General Assembly of the State of Indiana: It has been found that a circular area is to the square on a line equal to the quadrant of the circumference, as the area of an equilateral rectangle is to the square on one side. The diameter employed as the linear unit according to the present rule in computing the circle's area is entirely wrong, as it represents the circles area one and one-fifths times the area of a square whose perimeter is equal to the circumference of the circle. This is because one-fifth of the diameter fils to be represented four times in the circle's circumference. For example: if we multiply the perimeter of a square by one-fourth of any line one-fifth greater than one side, we can, in like manner make the square's area to appear one fifth greater than the fact, as is done by taking the diameter for the linear unit instead of the quadrant of the circle's circumference "Section 2. It is impossible to compute the area of a circle on the diameter as the linear unit without tresspassing upon the area outside the circle to the extent of including one-fifth more area than is contained within the circle's circumference, because the square on the diameter produces the side of a square which equals nine when the arc of ninety degrees equals eight. By taking the quadrant of the circle's circumference for the linear unit, we fulfill the requirements of both quadrature and rectification of the circle's circumference. Furthermore, it has revealed the ratio of the chord and arc of ninety degrees, which is as seven to eight, and also the ratio of the diagonal and one side of a square which is as ten to seven, disclosing the fourth important fact, that the ratio of the diameter and circumference is as five-fourths to four; and because of these facts and the further fact that the rule in prresent use fails to work both ways mathematically, it should be discarded as wholly wanting and misleading in its practical applications. "Section 3. In further proof of the value of the author's proposed contribution to education, and offered as a gift to the State of Indiana, is the fact of his solutions of the trisection of the angle, duplication of the cube and quadrature having been already accepted as contributions to science by the American Mathematical Monthly, the leading exponent of mathematical thought in this country. And be it remembered that these noted problems had been long since given up by scientific bodies as unsolvable mysteries and above man's ability to comprehend." ============================================================= The posting goes on to mention:
The Senate Journal mentions only that the bill was read a second time on Feb.12, 1897, that there was an unsuccessful attempt to amend the bill by strike out the enacting clause, and finally it was postponed indefinitely. That the bill was killed appears to be a matter of dumb luck rather than the superior education or wisdom of the Senate ....
/Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
Say what? It will take more patience than I possess to unravel this tangled tale sufficiently to determine if it implies that pi is three. E.g. what's a "line equal to the quadrant of the circumference"? On Sunday, May 11, 2003, at 11:46 America/Denver, Bernie Cosell wrote:
On 11 May 2003 at 9:12, Roland Silver wrote:
It is probably urban legend that bills have been introduced in one or another benighted state legislature to insure that pi is taught to be three to the kiddies thereof (one of the Benighted States of America? where all wheels are hexagonal).
This from a posting to sci.math by Allan Adler in 1991:
======================================================== "House Bill No. 246, Indiana State Legislature, 1897",
[...]
The author of the bill was Edwin J. Goodwin, M.D. It was introduced into the House by Mr. Taylor I. Record, Representative from Posey County, on Jan.18, 1897. The following is the statement of the bill:
"HOUSE BILL NO. 246
"A bill for an act introducinga new mathematical truth and offered as a contribution to education to be used only by the State of Indiana free of cost by paying any royalties whatever on the same, provided it is accepted and adopted by the official action of the legislature of 1897.
"Section 1. Be it enacted by the General Assembly of the State of Indiana: It has been found that a circular area is to the square on a line equal to the quadrant of the circumference, as the area of an equilateral rectangle is to the square on one side. The diameter employed as the linear unit according to the present rule in computing the circle's area is entirely wrong, as it represents the circles area one and one-fifths times the area of a square whose perimeter is equal to the circumference of the circle. This is because one-fifth of the diameter fils to be represented four times in the circle's circumference. For example: if we multiply the perimeter of a square by one-fourth of any line one-fifth greater than one side, we can, in like manner make the square's area to appear one fifth greater than the fact, as is done by taking the diameter for the linear unit instead of the quadrant of the circle's circumference
"Section 2. It is impossible to compute the area of a circle on the diameter as the linear unit without tresspassing upon the area outside the circle to the extent of including one-fifth more area than is contained within the circle's circumference, because the square on the diameter produces the side of a square which equals nine when the arc of ninety degrees equals eight. By taking the quadrant of the circle's circumference for the linear unit, we fulfill the requirements of both quadrature and rectification of the circle's circumference. Furthermore, it has revealed the ratio of the chord and arc of ninety degrees, which is as seven to eight, and also the ratio of the diagonal and one side of a square which is as ten to seven, disclosing the fourth important fact, that the ratio of the diameter and circumference is as five-fourths to four; and because of these facts and the further fact that the rule in prresent use fails to work both ways mathematically, it should be discarded as wholly wanting and misleading in its practical applications.
"Section 3. In further proof of the value of the author's proposed contribution to education, and offered as a gift to the State of Indiana, is the fact of his solutions of the trisection of the angle, duplication of the cube and quadrature having been already accepted as contributions to science by the American Mathematical Monthly, the leading exponent of mathematical thought in this country. And be it remembered that these noted problems had been long since given up by scientific bodies as unsolvable mysteries and above man's ability to comprehend." =============================================================
The posting goes on to mention:
The Senate Journal mentions only that the bill was read a second time on Feb.12, 1897, that there was an unsuccessful attempt to amend the bill by strike out the enacting clause, and finally it was postponed indefinitely. That the bill was killed appears to be a matter of dumb luck rather than the superior education or wisdom of the Senate ....
/Bernie\
-- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (4)
-
Bernie Cosell -
Eugene Salamin -
R. William Gosper -
Roland Silver