## Search Results for ‘168’

one has already learned the 7-cycle sunday-monday-tuesday-wednesday-thursday- -friday-saturday-(sunday-…) as part of one’s cultural heritage as an english speaker. and it’s high time i *used* that fact in studying “fano’s rainbow” (aka “the seven-point [projective] space”). and so to each of the *positions* in the well-known “three corners, three midpoints, one center” representation of fano space, […]

evidently felix klein nailed it long ago (i’ve been working on it on and off for years). scroll past the annoying animation: john baez on klein’s quartic. also: the eightfold way.

the seven black triangles are the blends Mud Yellow Purple Mud Red Green Mud Blue Orange the blurs Yellow Blue Green Yellow Red Orange Blue Red Purple and the ideal Purple Orange Green. the “theorem” in question is then that when the “colors” MRBGPYO are arranged symmetrically (in this order) around a circle (the “vertices”of […]

the color-scheme is inspired by one-or-the-other of a hyperbolic plane coloring & the simple group of order 168 (dana mackenzie; monthly of 10/95) or why is PSL(2,7) GL(3,2)?(ezra brown & nicholas loehr; monthly of 10/09)… okay, it was the mackenzie. but i want you to look ’em both up. the brown-loehr i’ve known longer and […]

the tetrahedral group at left: A_4, to the group-theory geeks. up top, the “yrb” labeling of the vertices of a cube, with the bit-string digital code and a 2-D projection. the seven-color theorem… concerning the simple group of order 168 & MRBGPYO… is hinted at. under that, as one can *kind of* read on the […]

{1, 2, 3, 4, 5, 6, 7} (“barred” inside the “big circles”… as they ought to be throughout) are here identified with { 001, 010, 011, 100, 101, 110, 111 } in the usual way (“binary arithmetic”). these objects — triples of zeros-and-ones — can of be considered as (so-called) 3-vectors: { (0,0,1), (0,1,0), (0,1,1), […]

okay. not so much a theorem as a simple brute *fact*… a perfectly *obvious* fact but one that i managed to overlook for years. (this kind of thing happens all the time of course.) **Directions let “clockwise” be the “positive” direction (for this post only; the usual [trig class] convention is to use the opposite […]

here’s the same group… call it G… appearing as the lower-left hex board from a set of four. we intend to display an accurate visual representation of the simple group (S) of order 168. our group (G) is one of many 7-element subgroups (this particular one is selected because \psi is easily memorized). what we […]

i signed on as a math teacher and became however good i am at it now over the course of a longer period than i like to think about. meanwhile, a lot of math departments have committed (e.g.) to require students to buy “graphing calculators”. the curriculum is adjusted accordingly. this not only does nothing […]

OK. Look. Last week’s rant was exhausting and I don’t want to make a career out of railing against this doggone book. But come on. How the bejabbers am I supposed to talk about inverse functions without a notation for the furshlugginer Identity Function? I mean, seriously.Consider the set of Real-valued functions of a Real […]