Search Results for ‘desargues’
the diagram is, essentially, traced from bruce e.~meserve’s _fundamental_concepts_- _of_geometry_ (dover reprint of 1983; originally addison-wesley 1959). but i added in the colors. with which, one has as follows. there’s a red line, a blue line, and a yellow line. to start with. all sharing a point. then two “triangles” are constructed: each of these […]
the MEdZ logo indicates where the ten lines of the desargues diagram fall. one has ten such lines. also ten points. each line can be considered as a set of three points; similarly each single *point* belongs to three *lines*. in fact, we have a “duality” here… theorems about points-and-lines remain true when the words […]
ten poles, ten polars, and ten pairs-of-triangles: ten ways to use one drawing (from MathEdZine, of course) to illustrate one theorem. (desargues’ theorem at w’edia.) performing calculations using actual blobs of color rather than alphabetical symbols *standing* for colors is time-consuming (and demanding of special tools)… but one literally “sees” certain things *much more readily* […]
somewhere in all this “desargues” stuff i claimed that i don’t have the skill to draw the “symmetric” version on the diagonals of a dodecahedron (or, equivalently, on pairs- -of-opposite-faces of an icosa… as shown here). well, now i can prove it. the notes are already posted i guess. i’m going on not much sleep […]
almost-symmetric desargues’ theorem. (7-color version) 5 “flat” and 5 “tall” triangles arranged as the 10 “intersection points” of a (so-called) pentagram. thus far the black-and-white “underlying diagram” (which i probably should have photographed before coloring it in and erasing it… it was the best b&w version i’ve done so far, i think… oh well…). the […]
starting with the mathy stuff on what used to be a door ( at the corner of what used to be a street: in “the livingston library”, or, more precisely, as i think of it, at the living- ston “branch of the UUCE” libe, where for “UUCE”, read th’ UU church in reynoldsburg [ohio; do […]
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 […]
two triangles are displayed here. each has a Red, a Yellow, and a Blue vertex. joining the red vertices to form a red *line*… and forming blue and yellow lines likewise… the triangles are arranged in such a way that the three lines so described meet at a single point. (two triangles chosen “randomly” from […]
cf the second, smaller, sketch is from desargues’ theorem in color (but let’s call it desargues’ rainbow from here on to match fano’s rainbow, posted the next day). in the first, newer, bigger sketch, i’ve used my mystical “projective geometry” powers to bend all the lines into circles. so we now (as you can see) […]
the livingston review 