d. Functions on the Domain of Shapes


At least one of the applets on this page leads to applets that were written for the Wolfram Demonstration Project. In order to run them you will need to download the Wolfram CDF reader [available FREE at http://www.wolfram.com/education/]

A geometric construction or a series of them may be thought of a function. Here is an example: Construct the three medians of a triangle. Reflect the point of concurrence of the medians over each of the sides of the triangle. These operations define a new triangle. Taken together these operations are a function from the domain of point triples in the plane to the range of point triples in the plane. This collection of applets allows for the exploration of such functions on shapes.

Topics include

  •         medians, altitudes & angles bisectors in triangles
  •         geometric generalization
  •         functions on triangles & quadrilaterals
  •         functions on rectangles, circles, ellipses
  •         polygons
  • transformations: translation, dilation, rotation, reflection, & combinations thereof
Polygons explorations [with some suggested applet sequences]
 
Seven
Functions on a Triangle
 
An interesting Function on the space of quadrilaterals


 

 '...in a square'

1
Point in an Equilateral Triangle

2

Point in a Square

1
Quadrature of the Rectangle
 



1

1

Overlapping Squares - reasoning about rates


3

Yellow bowties- reasoning about rates


Taking Sides

 3
Point in a Regular Pentagon

4

Point in an Equilateral Triangle - revisited


 2
Quadrature of the Triangle

 
Parallelogram Partition

2
Quad in a Quad

2
Overlapping cubes reasoning about rates

4
Overlapping Right Triangles


Four color Square

5
Polygon Explorer


Rotating squares - an algebraic perspective


Two Rectangles in a Square
 
3
Polygons in polygons



 1
Students define a median


Beyond the Median



Sum of polygonal areas

Yaglom's Road
 


Polygonal pancakes
 
4

 5
The Marion Walter Theorem
 
6
Generalizing the Marion Walter Theorem



1 quad
4 triangles
 

A Merry Go Round Triangle
 

Three angles
 

Napoleon's Theorem

Three Similar Triangles 
 
5
Aubel's Theorem


Polygon constructions

Sundry other [with some suggested applet sequences]

'Circling the Square'
 
Archimedes & the Volume of a Sphere

 
An homage to Archimedes

Hemisphere, cone, cylinder

1
Discovering Pythagoras
1
 
Square in a Regular Tetrahedron
 
Euler's
line
  
Why Radians?
 
A 3 dimensional
 Protractor ?
 
Area Perimeter Workbench

A circular conundrum
2
Discovering the Law of Cosines
1
Was Pythagoras wrong? - Related Heresies
2
 
sum of two reflections
 


Inscribing an isosceles triangle in an ellipse - II

 
 



3
Transformations II
A single rotation replaces a rotation & a
translation

 
The secret life of triangle medians & hexagon sides

 
A cube removed from a cube
 
Scaling the volume of a cone

 
 
Steepness - another road up a mountain
 
6 objects in search of conjecture(s)
 


 
Filling Revolutionary Vessels
 
 
 
The Most Efficient Can of Vegetables


 
 
 
 
Logs in a Trough
 
 
Two
napkin rings
 
A Gecko's Journey
 

 
 
 
 

  
 
Two Rectangles in a Square II
 



What do you now know more about?
What surprised you?
What would you like to know more about?

Judah L. Schwartz


Creative Commons License
mathMINDhabits by Judah L. Schwartz is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License..