elviszap.bsky.social
Retired Math Professor. Still learning. I remain a legend in my own mind.
60 posts
181 followers
339 following
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youtu.be/VTOLrPESlD0?...
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I am always happy to watch your math and rifle twirling videos. In the maths vids, you have said things much better than I ever could. Keep up the good work!
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Technology in service to secretarial services is only intended to make the secretary's life easier. In my experience as an editor, author, and reviewer, the editorial management system (TM) makes no one's life simpler.
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You are not being fair to manure which can be useful.
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Jeepers! I just gave a talk in which I spoke about both black and white vertices. Come to think of it, I also talked about birth and death. There were manifolds with boundaries that could have been called barriers.
CONTEXT MATTERS.
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May the floss be with you!
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To cogitate and solve!
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you are not being fair to anal orifices which serve a vital purpose.
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Sending my best thoughts to you and the nephew!
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If I am not mistaken, many of Euler's manuscripts are in translation on the ArXiv. But I am too lazy to check at the moment.
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The always amazing PSL(2,Z) !
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I'm old enough to remember having to fill out forms on paper with pen. In general, the problem described (death by 10^10 paper cuts) has been raging throughout my lifetime. Some malicious intent is present.
Otherwise, managers think, "Let me make my job easier," w/o thinking about your life
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Nah, Telsa's are/were popular in Austin. And so are Priuses. Interestingly I saw a chevy volt parked outside a warehouse district. I think the owner is a truck driver on a long haul.
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And that the integral of x^n b2 0 and 1 is 1/(n+1) is an expression of filling the (n+1)-cube with (n+1) pyramidal shapes upon half of the faces.
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you are just a youngster!
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Other gripes "It's a well-known fact." "One can show, ..."
(Who?)
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Indeed! As I was writing, I wanted to clarify, but I ran out of characters. And while I lean left politically, I also am left-handed, or more precisely, ambisinister. As a practical rule, I don't multiply inequalities through by negs and change signs. Instead, I reorder the terms. L2R.
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In re my confusions: 1st, distance on the line is spec. by squaring and then taking the sqrt. Vis: (x^2)^{.5}. A real no. squared is to the right. 2nd left is conventionally < . It's a cultural bigotry. As a lefty, I deal with it. I always use a < symbol when stating and solving ineq. ie 0<epsilon.
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When I was a student (late 1970s) calculators cost too much. To graph a function (plotting pts) was a struggle Calc. was a labor saving devise. Don't plot all points, plot those that matter. Precalc seems to be LEARN A CATALOG OF GRAPHS via applying the Interm. v. thm.
Not sure what is good.
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Yes lovely! Note also that, for example, 41x49=2009, 42x48=2016, 43x47=2021, 44x46=2024. So if two numbers have the same tens value and their ones add to 10, you can compute their product using the same trick you showed. And it's the same reason
(10n+a)(10n+(10-a))=100(n(n+1)n+a(10-a).
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Here is a revised number. Yesterday I walked about 3.5 miles in a little over an hour and 6176 steps were counted by my fitness app. The 0.8 meter stride was, on average too large, so the step count was too small.
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I think at my age, 68, I do a 20KM ride in about an hour. Maybe a little more. While my stride as a younger man was a 4 MPH walk, now it's closer to 3.5 MPH. Say 0.8 meters per stride, 0.8x1600=1280 steps per mile. So 4,480 steps per 3.5 miles, I guess give yourself 5000 steps for a 20K ride.
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Please visit my friend and collaborator's site:
www.nancyhocking.com to see what she is doing. Art and knots.
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Hmm, it seems that some brands of cat thy are a type of OULIPO writing in which actual objects and morphisms are excluded. ;-D
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As an aging adult,I taught myself to compute products of pairs of 2 digit numbers by differences of squares. I practice with 4 digit license numbers. Learn the squares from 1 - 100 by means of y'=2x. So eg. 39^2=1521. Then apply diff of squares. 40% of them are easy. Arith b4 alg.
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Finally, 3x97=291. So to test for div by 97, multiply the 1s place by 29 and subtract it from the priors. Consider, 9021. 902-29=873. 3x29=87. So 9021 is div by 97. Of course one might see that 9021=93x97 and 7221=83x87 b/c of diff of sqs. Time 4 some of my own math now b4 return for the proofs.
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To test div by 83: Multi the 1s place by 25, and add to the priors. Consider 7221: 25+722=747. 7x25= 175. 175+74=249. But 9x25=225. and 225+24=249=3x83. Another stable point. So 7221 is div by 83. To factor: 7221=3x2407. 240+21=261. 26+3=29. 7221=3x29x83. BTW, 29 is the 1st possible prime factor.
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So yesterday, after I wrote about 63, I had a computational misstep. To test for div by 73: Multiply the 1s place by 22 and add to the priors. Look at 219=3x73. 9x22=198. & 198+21=219. It's stable under this op. For 4891. 22+489=511. & 22+51=73.
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To test for div by 67, first multiply 67 by 3. The result is 201. So multiply the last digit by 20 and subtract the result from the priors. Look at 4891. 1x20=20, 489-20=469. 9x20=180. -180+46=134. 4x20=80.80-13=67.
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I hope you can see WHY they work. The WHY is not far from a proof. I am sure that tons of other people know this and these divisibility tests are "well known facts." That is written in a text book somewhere. A "Well Known Mathematical Fact" is like a famous mathematician. Oxymoronic isn't it.
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So that's the test for 43. Meanwhile, 3x47=141. So the test for 43 is the test for 141. Mult. the 1s place by 14 and subtract from the priors. Look at 53. 3x53 is 159. The test for 53 is to multiply the 1s place by 16 and add to the priors. I'll write out the other tests later.
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23,37,43,47,53,67,73,83,& 97. But note we found div'blty tests for some composites as well. So the test for 69 is a test for 23. To test for div by 37, mult. 1s place by 11 and subtract. (What's the test for 109?). Look: 3x43=129. The test for 129 is mult. the last digit by 13 and add to the priors.
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Div by 69: mult. 1s place by 7 and add to the priors. Div by 71: mult. 1s place by 7 and sub from the priors. Div. by 79: mult. 1s place by 8 and add to the priors. Div. by 81: mult. 1s place by 8 and sub. from priors. Div by 89: mult. 1s place by 9 and add to the priors. What primes are missing?
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I'll continue in a moment. But note that because of congruences, from 21, 39, 49, and 51 you get tests for 3 and 7, 3 and 13, 7 and 7, and 3 and 17, respectively.
Div. by 59: mult. 1s place by 6 and add to the priors. Div. by 61: mult. 1s place by 6 and sub from priors.
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Div by 31: Mult. the 1s place by 3 and sub from the priors. Div by 39: Mult. the 1s place by 4 and add to the priors. Div by 41: Mult. the 1s place by 4 and sub from the priors. Div by 49: Multiply the 1s place by 5 and add to the priors. Div by 51: Multiply the 1s place and sub from the priors.
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I think I see a pattern. Div by 9: Add the 1s place to the priors. Div. by 11: Subtract the 1s place from the priors. Div by 19: Multiply the 1s place by 2 and add to the priors. Div. by 21: Multiply the 1s place by 2 and sutract from the priors. ...
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Hmm. To test for div. by 71, multiply the last digits and subtract it from the priors. Again consider 4899. 489-63=426. 42-6x7=0. Or try 5183. 518-21=497. 49-7x7=0.
From the previous note 4899=69x71. And 23 quarters is $5.75. Test for div by 23? 57+35=92. And 14+9=23.
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To test for divisibility by 23, multiply the 1s place by 7 and add to the priors. So consider 4899. 9x7=63. 489+63=552. Repeat process. 2x7=14, 55+14=69. If you try this again, then 7x9=63, 63+6=69. So you have to know 69=3x23. But also, 7 is 1 mod 3. So you're also testing for div by 3.
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The tests that I have in mind are all the same. Multiply the 1s place by a number that is smaller than 1/2 the prime whose div'ity being tested. Then add (or subtract) to the remaining digits. If the result is div by the prime in question, so is the original number. Here are a few more tests.
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I'll quickly remind you the tests for div by 3,9 and 11. For 3 add all the digits, if the result is div by 3 then the number is div by 3. For 9 add the digits, if the result is div by 9, then the original number is div by 9. For 11 take the alternating sum of the digits analogous to an Euler Char.
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Whoops. 3x17x53.
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The 19s test is similar to one for 7. Double the 1s place and subtr. from the priors. For example 8281. 1x2=2, 828-2=826. 82-12=70. 70 is divisible by 7. Wait! there's a test for 49: multi 1s dig by 5 and add to the priors. 828+5=833. 83+25=98. 9+40=49. FWIW, 8281=91x91. Go on, test for div by 13.
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I guess I also learned of the test for div by 19 on the other place b4 it became a cesspool. Multiply the last digit by 2 and add to the priors. Take for example, 1596. Double 6, and add 159+12=171. 1x2=2, add to 17. You get 19. For the 19s test the number always reduces to 19. Cool, huh?
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Oh well, I guess we just have to know that 39=3x13.