February 2018 - mathfun@mailman.xmission.com

[math-fun] computation of Pi in hexa decimal
by Simon Plouffe 24 Feb '18

24 Feb '18

Hello, a certain Takahashi has computed Pi at the 10^17'th position in hexadecimal or 4*10^17 in binary using a cluster of pc's. It took 320 hours. You can send a request to the author to get a copy of the article, he sent me one. Also, I asked him if Elsevier is giving him any money for the 40 dollars they ask for 10 pages of text : No, het gets nothing. well, here is the article : http://plouffe.fr/simon/1-s2.0-S0167819118300334-main.pdf The hell with Elsevier, qu'ils pourrissent en enfer. This is a shame, Mr Takahashi is a respectable researcher using public money and taxes to write articles and the public gets nothing for that, mr Odlyzko was right, it does not get better over time. Best regards, Simon Plouffe

2 1

Re: [math-fun] student faces expulsion for joking that square-rootsymbol looks like a gun
by Henry Baker 24 Feb '18

24 Feb '18

Probably best to stay away from "Killing Fields", as well. https://en.wikipedia.org/wiki/Killing_vector_field In mathematics, a Killing vector field (often just *Killing field*), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric. At 04:09 PM 2/23/2018, James Davis wrote: >I'll avoid teaching the hermitian conjugation this semester. > >On Fri, Feb 23, 2018 at 4:34 PM, Hilarie Orman <ho(a)alum.mit.edu> wrote: >> And now teachers will get bonuses for being radicals. >> >> Hilarie

2 1

Re: [math-fun] student faces expulsion for joking that square-root symbol looks like a gun
by Henry Baker 23 Feb '18

23 Feb '18

California legislature has responded by outlawing "high capacity" roots -- those with bases > 3. A little-known clause in California's Bill also affirms Pseudo-Scotus, literally, "The (Federal) Supreme Court is fake". https://en.wikipedia.org/wiki/Principle_of_explosion At 12:53 PM 2/23/2018, Bill Gosper wrote: >https://www.truthrevolt.org/news/student-faces-expulsion-joking-square-root… > >--rwg

1 0

Re: [math-fun] Vacationing in France
by Dan Asimov 23 Feb '18

23 Feb '18

I lived near Paris for a year, but that was 45 years ago so some things have surely changed. Among the things that may not have changed: * Don't miss the great museums Jeu de Paume and l'Orangerie, fairly near each other; * Analogous to U.S. pizza, Parisians go out for couscous, a kind of pasta that looks like fat rice on which is served a delicious savory North African (chicken and/or beef) stew. The very best couscous imho is Algerian. And though it can be gotten in the Left Bank, the best I found is in the Right Bank (see this article: https://www.timeout.com/paris/en/restaurants/where-to-find-the-best-couscou…) * I used to like to hang out in an interesting area in the Left Bank called Place Contrescarpe. * Beneath much of Paris are underground passageways known as Les Caves. There are many food, music, and dance locations built in Les Caves (as well as many semi-abandoned miles of passages). * It's fun to hang out at a Paris café drinking beer or Pernod and have a paté sandwich while people watching. Some of the most venerable cafés include Le Procope, La Coupole and Le Select. (see https://www.tripsavvy.com/best-traditional-paris-cafes-and-brasseries-16183…) * If there's any chance you might like French cheese and wine, make sure to buy some bread, cheese, and wine and have some kind of picnic. There's nowhere else on earth that you can buy such a selection of great bread, cheese, and wine so cheaply! * Don't miss the English-language bookstore Shakespeare & Co., which has hosted many literary lights during the past century. A short walk away is the Notre-Dame cathedral, and a short walk from there are the "quais", the sidewalks along the Seine that have stalls selling books, pictures and other ephemera. * If you love good food, look up one-star restaurants in a Michelin guide — it can goe all the way up to three stars, but a one-star restaurant is already superb food. * If you rent a car (the French don't drive very safely, but at least they do it on the right side of the road) or otherwise, you might want to visit sights in the surrounding areas. I found this list at TripAdvisor (quoted in full with minor annotations: (https://www.tripadvisor.com/Travel-g187147-c4886/Paris:France:Trips.Outside…) It begins: ----- During longer stays in France (7 days or more), it's a good idea to arrive in Paris, stay for 2 or 3 days, take a day trip or a 3-4 day road trip, and end up departing from Paris. Generally, hotels and B&B’s outside of Paris are inexpensive. A resource for places to stay is Relais & Chateaux guide. ----- * Finally, I don't know what your French skills are, but I highly recommend making the effort to speak to French people in French (even if it means learning some French between now and your trip). Some French people might criticize your pronunciation (like the stereotype of Parisians), but many people will appreciate your trying to speak their language. Dan David Wilson wrote: ----- >I would like to visit Paris in April or June, probably for a week or so. >We'll want to see the famous landmarks, e.g. the Eiffel Tower, L'arc de >Triomphe, Notre Dame, &c. >We are in our late 50's, so I don't think we'll be hanging out at >nightclubs, though I would like to see the Moulin Rouge. >Fine dining is a must (secret gems, anyone?), and I want to hit a bistro. >Sharon will be interested in shopping (at least window shopping), I'm >thinking Montmarte is worth a day. >Perhaps I'll can drag her to the Louvre if it looks promising. > >My biggest concern is finding an economical to stay, and getting around. >I assume we want to see Paris on foot, and use the Metro to get around? > >I'm in the early planning stages. >I'll sift through your responses and start solidifying my plans. >Many thanks. -----

1 0

[math-fun] Unconditionally stable nesting coffee cups?
by Henry Baker 22 Feb '18

22 Feb '18

I don't know the answer to the following question, but it would be fun to come up with one. "Mathematicians turn coffee into theorems." -- unknown ?? I drink a lot of coffee, but when I shuffle papers on my desk, the coffee cup turns over & spills coffee all over the papers. Therefore, I'd love a cup design that is strongly resistant to turning over. This implies that the base should be larger than the top, and that the center of gravity -- even when full of coffee -- is very low. I also don't have a lot of room for storing coffee cups, so I'd still like them to _stack_ in such a way that they _nest_ & therefore don't occupy as much volume when stored. Finally, being a human, I'd still like to have a handle through which a finger could fit. The handle needn't touch in two places, so topologically it could be simply-connected. I envision some sort of "star-like" shape which will nest when the second cup is rotated 2pi/N. Like I said, I don't have a candidate shape.

14 22

[math-fun] Calabi Curlique Curve Curiousity
by Ed Pegg Jr 22 Feb '18

22 Feb '18

For six years, the product of the two Euler constants e×γ has given the highest temperature in the Curlique fractal. The value e×γ has a temperature of 2433.73 at 460024 steps. We have a new record. https://math.stackexchange.com/questions/69303/ The fundamental unit of the Calabi Triangle ratio, x^3+x^2−7x+1=0 with x≈2.10278... , has a temperature of 4408.7 after 2005399 steps. Can anyone get a higher temperature? --Ed Pegg Jr

3 2

[math-fun] xkcd CVE list today
by Hilarie Orman 20 Feb '18

20 Feb '18

In the otherwise wildly funny cartoon at https://xkcd.com/1957/ Randall Monroe strikes a bullseye with his computer vulnerabilities list but stumbles on basic math. Hilarie

8 14

[math-fun] Exponential function by limits approach:
by françois mendzina essomba2 19 Feb '18

19 Feb '18

Hello, A formula of this type is the following known formula: e^(z) = (1+z/n)^n ; n ---- infinity; I found the following formulas: 1) e^(z)=(2-sqrt(1-2*z/n))^n; 2) e^(z)=(3/2+(1/n)*(sqrt(13*n^6-30*z*n^3+36*z^2)/(4)+(12*z-5*n^3)/(8))^(1/3)-3*n/(4*((sqrt(13*n^6-30*z*n^3+36*z^2)/(4)+(12*z-5*n^3)/(8))^(1/3))))^(n^3); 3) e^(z)=(3/2+(1/n)*(sqrt(13*n^14-30*z*n^7+36*z^2)/(4*n^4)+(12*z-5*n^7)/(8*n^4))^(1/3)-3*n/(4*((sqrt(13*n^14-30*z*n^7+36*z^2)/(4*n^4)+(12*z-5*n^7)/(8*n^4))^(1/3))))^(n^7); 4) e^(z) = ((sqrt(36*z^2-30*n^17*z+13*n^34)/(4*n^14)-(5*n^17-12*z)/(8*n^14))^(1/3)/n-(3*n)/(4*(sqrt(36*z^2-30*n^17*z+13*n^34)/(4*n^14)-(5*n^17-12*z)/(8*n^14))^(1/3))+3/2)^n^17 ; and finally 5) e^(k)=((-sqrt((160*n^3*(h-r)^(1/3)-sqrt((9*(h-r)^(2/3)-8*n^2*(h-r)^(1/3)-12*n^4+48*k)/(h-r)^(1/3))*(9*(h-r)^(2/3)+16*n^2*(h-r)^(1/3)-12*n^4+48*k))/(sqrt((9*(h-r)^(2/3)-8*n^2*(h-r)^(1/3)-12*n^4+48*k)/(h-r)^(1/3))*(h-r)^(1/3)))/6+sqrt((9*(h-r)^(2/3)-8*n^2*(h-r)^(1/3)-12*n^4+48*k)/(h-r)^(1/3))/6+n/3)/n+1)^n^4 ; with: r : (192*k*n^2-176*n^6)/27 ; h : (8*sqrt(511*n^12-1380*k*n^8+1872*k^2*n^4-1728*k^3))/27 ; n ---- infinity; FME...

1 0

Re: [math-fun] Curved space paradox
by Don Reble 19 Feb '18

19 Feb '18

> Suppose we have a 3-dimensional space of constant, negative Gaussian > curvature. > > For some large enough R, construct the locus of points at distance R > from a fixed center C. ... an ordinary sphere. ... > Now, this sphere must itself have constant Gaussian curvature. Yes. > Select a point P on this sphere, and begin drawing circles of > increasing radius r on the sphere centered at P. > I mean r to be measured along the surface of the sphere, not straight > through the hyperbolic 3-space in which the sphere is embedded. > ...the circumference of a circle, centered at P, changes with its > radius r. For small r, it looks like 2 pi r. But as r gets larger, the > negative curvature of the ambient hyperbolic space begins to make > itself felt, and the circumference goes above 2 pi r... No. But it would, if r measures the radius that goes straight through the hyperbolic 3-space. > (If it doesn't, you didn't make R big enough -- that is exactly > what I meant by "large enough R" above.) Well: if the sphere is instead a horosphere, then it's surface is Euclidean, and the circumference is 2 pi r. If a hypersphere, the surface is negatively curved, and the circumference is above 2 pi r. A horo- or hyper-sphere has constant Gaussian curvature, but isn't a locus of points at distance R from a fixed center. --- Hmm... Let theta be the angle subtended by that curved radius at the sphere center C. Then the circumference is 2 pi r sin(theta) / theta regardless of the space's (uniform) curvature. -- Don Reble djr(a)nk.ca

1 0

Re: [math-fun] a numerical approximation close to 7 digit pi
by Dan Asimov 19 Feb '18

19 Feb '18

----- 355/113 is 6.57 decimal digits ----- Please explain how the / is .57 digits. (More seriously: Where does the 6.57 come from?) —Dan

8 9