Andrew Shipsides
January 31, 2002
Homework 1
My re-representation of the equation A2 + B2 = C2 consists of several hoops that
rotate around a common axis. In this case the center hoop, which has pegs coming out of
it, represents the equals sign. The outside hoops represent the right and left side of the
equations. On each hoop there are several rings – each of these rings represent elements
on each side of the equation. Concentric rings represent the squared function. When there
is more then one ring on a hoop the rings are added together. So on one side of the equals
element we have a hoop with two rings (concentric rings) – these ring represent A2 and B2
– and since these two rings are on the same hoop they are added. The other side of the
equals there is a hoop with one concentric ring – which represent C2 .
My representation has to be read in a certain way to understand but I think it’s
very natural. The equation is read along the bar or axis of my representation. Starting at
either the left or right side. When a hoop is found the elements or rings are then looked at
– and if there are concentric rings we consider that element squared – after looking at
these element we then move down the axis some more. In the case of my drawn image
read down the axis it equals A2 + B2 = C2 .
My representation is also scalable. To add more elements to the equation
represented we can simply add more hoops along the axis. To show the variable D is
equal to the A2 + B2 = C2 just add another equals hoop (hoop with pegs) and a hoop with a
single ring to represent D.
The reason I made this representation is because I was thinking about the torque
required to rotate each of the hoops. The equals hoops are used to represent two objects
