August 2012 - mathfun@mailman.xmission.com

Re: [math-fun] Is algebra necessary?
by Henry Baker 02 Aug '12

02 Aug '12

I.e., tail recursion. If bar is a function of one variable, wrapping a lambda(x) around it is useless & wastes stack space. In Common Lisp: #'(lambda (x) (bar x)) <=> #'bar At 04:58 PM 8/2/2012, Mike Stay wrote: >On Thu, Aug 2, 2012 at 4:44 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: >> Eta (I think this is the name?). Tail recursion. You can replace recursion by iteration in certain contexts. > >Eta is extensionality, i.e. any term T of type X is eta-equivalent to >(lambda x.T(x)) when x is not free in T and x has type X. >-- >Mike Stay - metaweta(a)gmail.com >http://www.cs.auckland.ac.nz/~mike >http://reperiendi.wordpress.com

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[math-fun] "Elementary/H.S." applications of quadratic formula?
by Henry Baker 02 Aug '12

02 Aug '12

I can easily come up with elementary applications of square roots, but are there any (many?) elementary/high school applications of the quadratic formula? The things I came up with are a bit artificial: cannon ball trajectories, drag strip race cars, bicycle wind resistance. I seem to recall some quadratic equilibrium equations from H.S. chemistry, but that isn't very elementary. (Helping to solve cubic eqns doesn't count!!)

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Re: [math-fun] "Elementary/H.S." applications of quadratic formula?
by Henry Baker 02 Aug '12

02 Aug '12

American Olympic sprinter LoLo Jones wears a necklace that sez Lo^2 See picture here: http://www.spikesmag.com/features/lolojonesonthestoryofthepicture.aspx http://en.wikipedia.org/wiki/Lolo_Jones So she clearly appreciates algebra. At 09:34 AM 8/1/2012, Mike Stay wrote: >On Tue, Jul 31, 2012 at 5:06 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: >> I can easily come up with elementary applications of square roots, but >> are there any (many?) elementary/high school applications of the quadratic >> formula? > >Most sports involve parabolic motion somewhere. Ask kids to estimate >Michael Jordan's hang time (the time in the air during a jump) and >you'll usually get answers ranging from a second to ten seconds; >they're really surprised when you ask them to count during a video. >There's a simple mat in many gyms that will measure the height of your >jump by timing it; it's a puzzle at first to figure out how it knows >how high you jumped, since there's no laser rangefinder or anything >like that. It's also very visceral. >-- >Mike Stay - metaweta(a)gmail.com >http://www.cs.auckland.ac.nz/~mike >http://reperiendi.wordpress.com

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Re: [math-fun] We don't need no stinking algebra
by Dave Dyer 02 Aug '12

02 Aug '12

> >The responses were all "duh! You press the 'sin' key! ...So since we >can do that, Yes, but suppose you were shipwrecked on a desert island with nothing but a sextant, a digital watch, a slide rule, and ONE bottle you could cast into the sea with your latitude and longitude written on it.

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[math-fun] name for 1/8 of sphere
by James Buddenhagen 31 Jul '12

31 Jul '12

A friend who is a sculptor asked me if there is a name for the shape of the 8 pieces a solid sphere would fall into if you cut it with 3 mutually perpendicular planes through the center. I couldn't think of any but thought I would ask here. And more generally, is there a name for a 'spherical wedge' bounded by a spherical triangle and the planar faces from the center containing the triangle's edges? Thanks for any help on this. Jim

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