Responding to a geometry problem, Gemini experimental 1206 started out with
Here's a solution to the problem, along with a diagram to help visualize the steps:
**Diagram**
[asy]
unitsize(0.5 cm);
pair A, B, C, D, E, F, G, O;
A = (0,4);
B = (0,0);
O = (A + B)/2;
C = (5,0);
D = (8,4);
E = extension(A, D, C, reflect(O,C)*(A));
F = foot(O,B,C);
G = foot(O,A,D);
draw(A--B--C--D--cycle);
draw(A--C);
draw(Circle(O,abs(O - A)));
draw(O--F);
draw(O--G);
draw(O--E);
label("
AA
", A, NW);
label("
BB
", B, SW);
label("
CC
", C, SE);
label("
DD
", D, NE);
label("
EE
", E, dir(0));
label("
FF
", F, S);
label("
GG
", G, W);
label("
OO
", O, W);
label("
44
", (O + B)/2, W);
label("
45∘45∘
", A + (0.8,-0.3));
label("
88
", (A + C)/2, SE);
[/asy]
**Solution**
There are some observations:
- The asymptote code didn’t come with the usual " Use code with caution." footer.
- It’s a very good idea to generate diagram code, but it needs to work. The code fails to compile, it issues the error message
F = foot(O,B,C);
^
workspace_1.asy: 10.5: no matching variable 'foot'
because a required import is missing. Easy to fix, similar to Gemini forgetting to import numpy as np.
However, it also generated an invalid character, so there is another error
This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2022/dev/Debian) (preloaded format=latex)
restricted \write18 enabled.
entering extended mode
LaTeX2e <2021-11-15> patch level 1
L3 programming layer <2022-01-21>
(./workspace_1_.tex (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2021/10/04 v1.4n Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo))
(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty)
(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty)
(/usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/graphics.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/graphics-def/dvips.def)))
(/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-dvips.def)
(./workspace_1_.aux)
! LaTeX Error: Unicode character ∘ (U+2218)
not set up for use with LaTeX.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.154 }
%
The correct character to use for the degrees is 45°.
In the text following (the text generated after the Solution heading), the model assumes the user can see the drawing. And it should. But that means, the generated code for the drawing needs to actually work.