3D MODELING
VISUALIZING IDEAS
Vertical Steam Engine
Using SolidWorks software, we digitally reconstructed this vertical steam engine from hand-drafted drawings.
Sterling Engine
A group of us at UI built this miniature Sterling engine in the shop. (I made the bent levers which are blurred with speed here, and a couple of the internal parts.) It runs quite well.
Sterling engines are interesting - they 're still waiting for their time in the limelight. I enjoyed this description of the original invention:
"Some historians have indicated that the reason for Rev'd Stirling's efforts at such a device were driven by his concern for the working people of his parishes as steam engines were being used extensively in that area and time period. Due to the lack of strength in the materials available to construct boilers ('Bessemer Iron', or Steel, was not yet available), they would frequently explode with devastating results on the people working nearby...
So Rev'd Stirling invented a safer (and more efficient) replacement for the steam engine, in order to save lives and improve the conditions of his parish life. Stirling's engine would not explode because the pressures were not elevated to that level. The machine simply stopped if the heater section failed. " --- Stirling International.org
Multiplication Tables
If you are bored, get out a piece of paper, draw a circle, and number points around its perimeter. (200 is a good number of points to start with.) Then connect the points with lines according to whatever multiplication table you choose. For example, if you choose the 2x table, connect 1 to 2, 2 to 4, etc. Strange patterns will emerge, many of them very beautiful.
I was introduced to this by Mathologer on YouTube: https://www.youtube.com/watch?v=qhbuKbxJsk8
(The video is very good, watch it if you have a chance.)
I wrote Matlab code to experiment with the different multiplication tables. Feel free to use it! Note: use whitebg('w') to set your background back to white.
81 x
2 x
%draws the multiplication table
r=1; %radius
x=1; %x coordinate center
y=0; %y coordinate center
c=81; % multiplication factor
th = 0:pi/100:2*pi; %angle
xunit = r * cos(th) + x;% x coordinate set
yunit = r * sin(th) + y; % y coordinate set
h = plot(xunit, yunit); % circle plot
hold % stay on same plot
% This section adjusts matrix size appropriate for given c
xunit2=xunit
yunit2=yunit
for j=1:c
xunit2=[xunit2,xunit];
yunit2=[yunit2,yunit];
end
% This set makes a solution set connecting points to their multiples
for i=1:length(th)
a(:,i)=[xunit2(i);xunit2(c*i)];
b(:,i)=[yunit2(i);yunit2(c*i)];
end
whitebg('k') % makes background black
%set(gca,'color','r') %thought this might be useful to know how to use
plot(a,b)