Complete issue 30:3 as one pdf - TUG
Complete issue 30:3 as one pdf - TUG
Complete issue 30:3 as one pdf - TUG
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TEX Education EUROTEX 2009 E27<br />
z3 moveto z4 lineto z1 lineto<br />
top moveto z1 lineto<br />
top moveto z3 lineto<br />
top moveto z4 lineto stroke<br />
top moveto z2 lineto<br />
[2]1 setd<strong>as</strong>h stroke}def%end pyramid<br />
%<br />
<strong>30</strong> <strong>30</strong>0 translate<br />
0 0 1 setrgbcolor%blue<br />
1 setlinecap 1 setlinewidth<br />
%<br />
15 25 65{/a exch def<br />
<strong>30</strong> -20 10{/b exch def<br />
pyramid<br />
57 0 translate}for}for<br />
showpage<br />
Escher’s impossible cube<br />
As student I w<strong>as</strong> <strong>as</strong>ked by my professor to (re)make<br />
Escher’s 25 Impossible Cube.<br />
I decomposed it into two parts, in timber, and put<br />
them together such that in projection the impossible<br />
cube w<strong>as</strong> obtained. I photographed it and handed the<br />
photo to my professor. 26<br />
I’m happy that after so many years, I had the guts to<br />
emulatethe cubes.<br />
I consider each corner of the (impossible, nonmathematical)<br />
cube <strong>as</strong> a cube itself, with its 8 corners<br />
<strong>as</strong> data points, which yields in total 64 data points.<br />
After projection I could connect the appropriate points<br />
and make the (impossible) cube. First, I did the er<strong>as</strong>ing<br />
and adjusting in Photoshop, but a little later I drew the<br />
impossible cube in PS al<strong>one</strong>, which is not completely<br />
general <strong>as</strong> function of the viewing angles. A bit tedious.<br />
The code is too long and too tedious to be included<br />
here.<br />
Gabo’s constructive art<br />
Long ago, I w<strong>as</strong> still a student, I visited the Tate Gallery<br />
inLondon,andw<strong>as</strong>captivatedbytheconstructiveartof<br />
Gabo, 27 especially his lineariiofthe early 1940-ies.<br />
NaumGabo<br />
← Lineari<br />
→ Linearii<br />
I also p<strong>as</strong>sed by his (temporarily nonworking) fountain<br />
in front of the St Thom<strong>as</strong> hospital opposite the Big Ben,<br />
onthe otherbankofthe river Thames.<br />
In the fountain, the regular surface is formed by jets of<br />
water, and changes dynamically, because it rotates, due<br />
to the ‘action isreaction’ principle.<br />
Aftermanyyears,Iallof<strong>as</strong>uddenhadanideaofhow<br />
to imitate this fountain in my garden, for my quarter<br />
circlepond.Averyremotesortofimitation,but...funny.<br />
Too alternative to be included here, maybe on the slides<br />
forBachoTEX2010,forfun.<br />
With my youngest daughter I imitated Gabo’s linearii<br />
inpl<strong>as</strong>tic.<br />
In ≈1995 I emulated lineari, linearii in MF, and<br />
adapted the code towards MetaPost. For this conference<br />
I looked at the pictures again. Sveta and I adjusted them<br />
withthinner lines andcolored themblue.<br />
Theycameoutmorebeautifulthanbefore,evennicer<br />
thanthephoto’softheobjects, IMHO.Amatteroft<strong>as</strong>te?<br />
NaumGabo<br />
Lineari
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