A Rhyme for the Pythagorean Theorem
This is a math kind rhyme about three spacial toads
they each live in a house that is two dimensional
their houses are all built the same in each and every way
except their sizes differ somewhat and so I'll ascertain:
their similar
proportional
parts can be compared
|
|
Figure 1
The roofs of these three houses are right triangular
the walls of these same houses are built as perfect squares
now this little lema's gonna help us have some fun
'cause it'll let us know a theorem called the Pythagorean
ancient Greek
right triangles
hypotenuses
|
|
Figure 2
Construct a right triangle with sides G H and I
then drop a ray from the right angle through the other side
this new ray needs to follow one important rule:
it must intersect with a right angle the hypotenuse
two new triangles
three in all
four is too many
|
|
Figure 3
If both of the new triangles have angles that are square
and both have common angles with the first we can declare:
these three right triangles are all similar it's shown
and they could be the roofs of our three toads' flat world homes
similar houses
similar triangles
tree frogs
|
|
Figure 4
The names of our three toads today are Jimi, John and Joe
You can see which house each lives in on the diagram below
you'll note John's roof and Joe's roof combine to form old Jim's
ergo John's square and Joe's square sum to the square Jim must live in
sum of squares
beautiful
Pythagorean
|
|
Figure 5
|
