March 2015 - mathfun@mailman.xmission.com

Re: [math-fun] supersupersupersuper nova
by Henry Baker 05 Mar '15

05 Mar '15

Ok, so what % of this "ground hog day" universe is merely a reflection/refraction of some other portion? What if our telescopes are essentially kaleidoscopes? We recently learned from "Interstellar" that rotating black holes map their backgrounds into fractal patterns reminiscent of Newton iterations. What if a significant fraction of the light that we see in the sky is coming from the same places, but at different times? After all, if there is so much dark matter, it should be capable of quite a bit of lensing. At 02:21 PM 3/5/2015, Warren D Smith wrote: >A supernova exploded. It then appeared 4 times in 4 places in the sky. >This seems to prove gravitational lensing happens... in case anybody >doubted it, it now seems a lot more proven. The relative time delays >are of order 10-100 years and more images of it will probably come to >those who wait >another 10-100 years. > >http://www.eurekalert.org/pub_releases/2015-03/uoc--dss022515.php

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[math-fun] supersupersupersuper nova
by Warren D Smith 05 Mar '15

05 Mar '15

A supernova exploded. It then appeared 4 times in 4 places in the sky. This seems to prove gravitational lensing happens... in case anybody doubted it, it now seems a lot more proven. The relative time delays are of order 10-100 years and more images of it will probably come to those who wait another 10-100 years. http://www.eurekalert.org/pub_releases/2015-03/uoc--dss022515.php

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Re: [math-fun] newton rotating liquid mirror
by Henry Baker 05 Mar '15

05 Mar '15

A focal length of the Earth to the Sun would be an interesting telescope; long focal lengths aren't out of the question; NuSTAR's X-ray telescope has a focal length of about 33'. Has anyone considered a telescope with a focal length of perhaps the Earth to the Moon? https://en.wikipedia.org/wiki/NuSTAR At 12:27 PM 3/5/2015, rcs(a)xmission.com wrote: >the focal length of the mirror would be about 1/4 of an astronomical unit (distance from Earth to Sun).

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[math-fun] liquid mirrors
by Warren D Smith 05 Mar '15

05 Mar '15

As I (vaguely) recall, you got one of those wide shallow cookie tins, put a plastic bag inside, put plastic resin inside mixed with some kind of colorant, got it spinning on the phono turntable, added hardener catalyst. (And all with a lid on to avoid wind from passing air.) Or for nonpermanent, use water mixed with ink. The earth is not flat, causing parabola, not really to be. This is not problem since earth large, but would be a problem for an asteroid. Also, ripples in the liquid, surface tension, nonuniform g-field, etc, all would be a serious problem in a very weak g-field of some asteroid. In an inverse square law g-field, y=altitude, r=distance from spin axis, neglecting surface tension and self-gravitation, the equipotential surface is C=sqrt(r^2+y^2)*(B+A*r^2) where A,B,C constants, which is y^2 = (-A^2*r^6 - 2*A*B*r^4 - B^2*r^2 + C^2) / (A^2*r^4 + 2*A*B*r^2 + B^2) which as you can see is not at all a parabolic curve, it is degree=6... but whatever it is, is locally parabolic. In practice when this method is used to cast giant glass mirrors in rotating furnace, I suspect the biggest problem is thermal stresses. They need very slow cooling to try to avoid this problem -- months. They cast them with a custom mold below intended to create honeycombed beam structure of the glass on the other side of the mirror, so it is stiff and strong. It occurs to me that a perhaps better idea would be to place the liquid glass on top of liquid tin within the rotating furnace. Then perhaps it would be possible to cool it much more quickly. The resulting mirror then would be smooth on both sides and look a bit like an eggshell. The beams would be absent, but could be replaced by external beams I suppose.

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Re: [math-fun] newton rotating liquid mirror
by Henry Baker 05 Mar '15

05 Mar '15

Couldn't we build such a mirror at the South Pole using just the Earth's rotation? It would want to be pretty big, but there's lots of open space down there. Even if you didn't care about visible light wavelengths, you could still provide a bunch of liquid-filled tubes to distribute the correct height to each location where you could put a small radio antenna. Alternatively, you go through the asteroid belt to find a decent size spinning asteroid and install your mirror there. Yes, you don't have much control over where it points, but there are some types of investigations where that might not matter. At 08:56 AM 3/5/2015, Warren D Smith wrote: >Adam P.G's blog seems amazinger and amazinger. >I don't understand his life census, but it too seems amazing. > >I noticed some post by him about the spinning liquid parabolic mirror being invented by >Isaac Newton. I actually made one of those mirrors once using a phonograph turntable >and plastic resin. The mirror was quite decent, although I daresay it >was not good enough for a quality telescope. A lot of people may be >willing to donate an old phonograph turntable no longer useful to them for music.

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[math-fun] newton rotating liquid mirror
by Warren D Smith 05 Mar '15

05 Mar '15

Adam P.G's blog seems amazinger and amazinger. I don't understand his life census, but it too seems amazing. I noticed some post by him about the spinning liquid parabolic mirror being invented by Isaac Newton. I actually made one of those mirrors once using a phonograph turntable and plastic resin. The mirror was quite decent, although I daresay it was not good enough for a quality telescope. A lot of people may be willing to donate an old phonograph turntable no longer useful to them for music.

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[math-fun] pi
by meekerdb 04 Mar '15

04 Mar '15

The ultimate pi day, 3/14/15, of the century is only a little over a week away. Any good recipes you'd like to share? Brent

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[math-fun] natural numbers
by Warren D Smith 04 Mar '15

04 Mar '15

I like "Z" with subscript (or superscript) ">=0" or Z with subscript ">0" depending what you want. "N" usually seems stupid by comparison. (How about "U" for the "unnatural numbers"?) For some reason I'm not too horrified by "Q" to denote the rationals instead of (say) "Z/Z" which seems less wasteful.

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[math-fun] Fractional emoji
by James Propp 04 Mar '15

04 Mar '15

Here's an emoticon I just coined (maybe others have already invented it) in texting my brother: :-) / 2 It means "half-kidding". Jim Propp

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Re: [math-fun] 1 l I | 0 O log ln lg
by Steve Witham 04 Mar '15

04 Mar '15

Funny, while reading about how lowercase L, capital I and numeral 1 all look so similar, I am seeing it in my email font where they're entirely different, and all distinct from the vertical bar. It can be done. Lowercase L, by the way, looks like this: -+ | | | | | \_ What I mean is, that is the actual, true appearance of lowercase L, which has only recently been discovered, apparently. I think in a pinch you can leave off the serif at the top. Here are some modern fixed-width fonts that follow the same conventions for 1, l, I and |, and similar differences between capital O and zero 0. Apple Menlo Bitstream Vera Sans Mono Bera, for use with LaTeX DejaVu Sans Mono I guess the reason there are more fixed-width fonts with these graces is that there are more programmers than mathematicians, and programmers... think of notation as malleable and utilitarian?. Be unambiguous and explicit, I say. That's why I like ln and lg. Also, check out http://www.johndcook.com/blog/2013/04/23/why-j-for-imaginary-unit/ . --Steve

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