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Lecture 14

A chalkboard as the professor left it: Euler's formula derived step by step from the Taylor series, braced, starred and boxed in yellow.

Lecture 14, a slate chalkboard after a lecture deriving Euler's formula from the Taylor series, with braces naming the terms, a boxed result, a unit-circle sketch and erased ghost writing
Click the picture for the full-size render.

How it is made

Three sliding slate panels carry one derivation. The Taylor series are recalled with braces under the first terms naming the n each comes from, and the powers of i set in two columns with a rule mod 4. Then x = iθ is substituted, the = where the signs flip starred and answered in pink, and the series regrouped, a blue brace under each bracket naming it cos θ or sin θ, before the result is boxed twice in yellow. A freehand unit circle, the quarter turns tabled in wandering columns, and Euler's identity circled finish it. The formulas are lib/mathkit.ps layouts (\underbrace, \overset, \pmod, aligned columns with /ColumnWander, and mkbrace) inked with lib/drychalk.ps's dcchalk, on dcboard panels that still carry the last lecture (the Gaussian integral and a bell curve) as ghost writing under eraser swipes. The hand leans further and loosens panel by panel.

Details

Category
Drawing (dry media)
Tags
chalk math
Libraries
artkit, drychalk, drykit, handscript, mathkit, paintkit, strokeglyphs
Added
2026-10-14
Built in
issue #238
Page size
1440 × 850 points

Source

View source the whole program in a scrolling window, or read gallery/chalkboard_lecture.ps on GitHub. To draw it yourself, from a checkout of the repository:

pscat --page 1440x850 gallery/chalkboard_lecture.ps
The first 40 of 325 lines of the source 
%!PS-Adobe-3.0
%%Title: Lecture 14 (a chalkboard after the lecture)
%%Creator: pscat gallery (issues #238, #532)
%%BoundingBox: 0 0 1440 850
%%EndComments

% A slate chalkboard as a professor left it after the lecture: Euler's
% formula derived from the Taylor series, across three sliding panels.
%
%   left    the Taylor series of e^x, cos and sin, recalled, the first
%           terms braced with the n each comes from, and the powers of i
%           in two columns, repeating mod 4
%   middle  x = i theta substituted, the = where the signs flip starred
%           and the star answered in pink, then the series regrouped, a
%           brace under each bracket naming it cos or sin, and the result
%           boxed in yellow
%   right   the unit circle sketched in the complex plane, the quarter
%           turns e^{i pi/2} ... e^{2 i pi} in two wandering columns,
%           Euler's identity circled, and the homework in the corner
%
% Under the fresh chalk lies the last lecture (the Gaussian integral and
% a sketched bell curve), erased under eraser swipes and finger wipes.
% Dust lies along the ledge and in the tray. The lecturer starts fresh
% and presses hard. By the right panel the hand is quicker, looser and
% lighter, except where the result is boxed.
%
% Everything is lib/drychalk.ps (dcboard, dcchalk) over drykit, with
% the formulas laid out by lib/mathkit.ps and the words written with
% lib/strokeglyphs.ps. No alpha, so Ghostscript renders it too.
%
%   pscat --page 1440x850 --png chalkboard_lecture.png gallery/chalkboard_lecture.ps
%   gs -dSAFER --permit-file-read=lib/ -sDEVICE=png16m -r72 -g1440x850 \
%      -o chalkboard_lecture.png gallery/chalkboard_lecture.ps

(lib/artkit.ps) run
(lib/paintkit.ps) run
(lib/drykit.ps) run
(lib/handscript.ps) run
(lib/strokeglyphs.ps) run
(lib/drychalk.ps) run

On GitHub