Some Seemingly Mathematical Recreations

Number Man

Can you do this picture of Math E. Matics?  Freehand, numbers only.

Practice a few times and you may even be able to imagine some expressions.   This one looks serious and professorial.     Try for an impression of a challenged student!









Is anyone old enough to remember Pac-Man?    Think about how to produce this one.

Graphing Calculator 4.0 was used to do this version.  Other tools will work.

We began with a circle of radius 7 centered at (0,0).   The eye was a circle of radius 1 centered at  (2,5).    ETC.



Begin with an equation for an ellipse:   . Change the equation to:    ?

Explain the result.

Paste the image of the heart into a GSP file and add the Arrow. 


The result may be a Valentine.













Bloated Polygons

Consider a square with a quarter circle inscribed from each corner:

In the center, the Figure bordered by the four arc is a Boated Square

Further exploration could examine, for example, the area of the bloated square relative to the generating square.

Create your own Bloated Square. Click HERE for one GSP file to create a bloated square.   (You may be able to find an alternative.)

Explore other bloated quadrilaterals where the generating quadrilateral is NOT a square.

The Bloated Triangle generated from an equilateral triangle has larger area than the generating triangle:





GSP files to explore Bloated (or collapsed) polygons

Equilateral Triangle.GSP

Variable Equilateral Triangle.GSP


Variable Square.GSP

Regular Pentagon.GSP

Variable Regular Pentagons.GSP

Regular Octagon.GSP

Why doesn't this one produce a bloated regular octagon?   What needs to be changed?

Maybe more to be added . . .