COPYRIGHT NOTICE
Copyright 2007 Samuel Dagan
dagan@post.tau.ac.il
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Pythagorean theorem
Proof of the Pythagorean theorem, as an example of a
figure-window
The origin of the figure is at (0,0)
© Samuel Dagan
abcc
c
ab c
cc
b²-a²
b²-a²+2ab
b²+a²-2ab
b²+a²-2ab
c²-ab
Pythagoras
Any Fig.window opens with two
rectangular parts: The control bar on the
top and the graphics below.
The leftmost top corner of the control bar
coincides with the leftmost top of the window,
and remains motionless,
independently of any resizing by the zoom of your system.
Try it!
The control bar contains
interactive buttons presented by yellow rectangles.
The mouse cursor becomes an index hand on an active button.
When a
button becomes inactive, its colour
turns to white and its wording is
changed occasionally. The restart
button reloads the whole window, but
keeps any resizing and panning done previously. The
next button provides
the next step. Be alert always of any active button for interactivity.
The Graphics implements panning
by dragging, and zooming by the wheel
of the mouse, as done in Google maps. Both are not
affecting the control
bar itself, but are needed for a more
detailed look of the graphical presentations. The inactive buttons now:
"pause","fast" and "slow", from the animate
part of the control bar, will become active, as we'll see in the
animation, that follows. Their meaning are self-evident, just exercise them in order to get familiar with.
Some times, in order to increase interactivity, additional buttons
are introduced in form of yellow rectangles or
disks. One such example is shown in the animation that follows.
A right angle coloured triangle is
displayed.
The hypotenuse also serves as the side of a square. The area of the
square is
c², and the area
of the triangle is ab/2.
We want to prove that c² = a² + b². The display
will rotate, and
then the square will be filled up with
triangles.
Use this animation to
experiment the "animate" buttons.
Four triangles cover the area of the
square, except leaving a small space.
What is its area in terms of a, b, c?
In order to interact with the user,
four yellow rectangular buttons, are added. Each one
contains an expression, but
only one of them represents the area of the
empty space.
Click on the button that
seems to
contain the right area. On
wrong answer, the button will vanish. Continue,
till you get it right.
Your score =
points,
out of 10 possible. The rest of the proof is a trivial
exercise.
restart
Use the zoom of your system
to resize this window
Use the mouse to pan and
to resize the graphics
ani-
mate
pause
resume
fast
slow
pause
fast
slow
next
next
end