Just because Randall showed/implied ? the waterman as a possible Cahill rip-off does not make that true...
Cahill polyhedra base is identical to the root 2 depictions.
Waterman sphere packed base is identical to the root 5 depictions.
just please have a look at this one page....do you see that these are not the same...the root 2 and root 5 ?http://paulbourke.net/geometry/waterman/index.html
So..it seems that I need to defend, what I now perceive, is an attack on my character , as in, ripping off the Cahill 1909 map with a simple plopping of Antarctica together...well since you raise the issue...
i worked in decoding the metrics of pack spheres for many years, starting around 1988 and then realized that they extrapolated into symmetrical polyhedra,
I then had all those shown on Paul's Bourke page to select from to project upon. One handled land sinus best, when it was rotated around the z axis by 20 degrees...so, i used that waterman root 5 to manifest, first...an equal line delineation projection ( as per my 1996 poster ) and a gnomonic projection ( as per 2011 ) so that i could tie into satellite imagines...which just recently has been accomplished. Only after that 1996 version was being sold, did I even ever hear of Cahill, as it so happens, and not that that actually matters. Later I had like 100 unlimited series of watermans to chose from...and still the w5 fcc swept from 0,0,0 remained/remains best!
My basis is understanding the math behind pack spheres and hence polyhedra generated from various clusters. Here are other maps/choices done on waterman polyhedra by Izidor Hafner. indeed I have a couple hundred different maps like those below.http://www.watermanpolyhedron.com/CART2dmaps.html
and i have new gored globes as rotatable 3d waterman polyhedra complete with countries with color.http://watermanpolyhedron.com/2011IH1.html
hardly a rip off or copy or a parody or the other "internet" slur you throw at me. i really find your little comment as ugly.
But hey, you will just dismiss me likely...without checking any of these links.
I do understand the oddity...no one has ever started from sphere packing...most pick known polyhedra...as Cahill did (Platinic solid, the octahedron )...
and as Fuller did twice...
( first with the cuboctahedron....my root 1 of that same page above, and then with the Platonc solid, the 5-fold, icosahedron )
However, it order to minimize the land breaks in large masses, he needed to offset his poles...neither to a face center nor a vertex. In consequence,
the shape of important referqnce lines is effected.
Izidor Hafner has done all the standard polyhedra...http://matematika.fe.uni-lj.si/people/i ... rious.html
land sinues, land sinues, land sinues...none of those work as well as the w5, either.
Note...i have some 20 years of hand-made artifacts depicting that journey...sphere packs polyhedra other globes, like a w42, and well more stuff and paper and graphs than seems possible. However, you are at liberty to believe what you want. My life has been about the work, not it's promotion...that only gets me side-tracked to the work. My real work, i believe is in physics. Even saying that word..makes all my math and sphere pack work hugely suspect. I only got into physics following the path of sphere packing math. This is what i do, and who I am. i gave up on maps for many years, because i felt that i had more work to do outside of cartography using waterman polyhedra. i am 10 times more dedicated in physics than cartography...and about 1/10 the feedback as i ever had in cartography. No, make that 1/100th. This too does not invalidate my physics theories. I looked through some physics stuff here and doubt i will start discussion on any of it. Much of my physics work is sphere pack based and most importantly...mathematical...and presented on my site.
like it or not, having an understanding of math of sphere packing is like newton having his calculas...one can look at things very differently, and can answer some questions differently mathematically...i can construct whacks of new symmetrical polyhedra with it..i can investigate a nucleus with it...perhaps paramount to all that..I can ask some really good Physics questions. So now you have double cause to dismiss me, cartography and physics...they are like totally subjective. However, my math can not be defeated by subjectivity in either of those arenas, and being math..can either be proven or not. Math is my tool/genius, not in stealing Cahill's simple design nor simple math. Tomorrow is another comic, and this thread seems to been ending most rapidly and quite poorly...and surely talking ABOUT Physics should seal its fate. Remember this was not about my work, it is about defending your accusation that my map was basically derived from Cahill's. My numerous derivative artifacts can speak for themselves...including MY w5 maps. and hundreds of other unique maps and globes. i am now quite used to people pulling this crap on me. Ignoring the math, and go after me personally...i have heard it all dude, though this accusation of using cahill map is a new tactic...usually i am told that i am confused and do not understand...while they refuse to talk math. i recognize this current tempo and know this thread will only deteriorate further. So I offer no more cartographic input and will sadly only respond if further personally attacked on this public forum. All in all, i only have thanks to Randall for bringing up the issue...is the waterman projection really just the cahill projection ?
I am curious if Randall will rectify his implication with a another comic ( someday ). Does he indeed, now feel the implied was/is unmerited.
I do not request a retraction, but would surely appreciate some rectification, if deemed appropriate.
So I am officially done with this thread.
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."