Thursday, May 9th

[Lara Hulbert]

Check out the grid below. You may wish to print it out. The upper left dot represents a rectangle with area of 12 and perimeter of 4. The lower right dot represents a rectangle with area of 4 and perimeter of 12. First step: Draw these two rectangles. What are their side lengths? Second step: Draw some more rectangles of whatever dimensions you choose. Find their areas and perimeters. Then plot your rectangles on the grid accordingly. Third step (question time!): What points on this grid are impossible points? What points are squares? Extra credit steps: And if you're feeling ambitious, what points are circles, what points are regular triangles? Regular hexagons?

[joshuaw.bartlett]

 

Sides on rectangle A do not exist.  Roots are +/- sqrt(11)i.

Sides on Rectangle B are 5.236 x 0.7639

 

Area = A, Perimeter = P

 

The points with impossible results are anywhere the A > 0.0625P^2

Squares reside on the line A = 0.0625P^2

Circles on the line A = P^2 / 2(pi)

Regular triangles on the line A = sqrt(3)/36 * P^2

and Regular hexagons on the line A = sqrt(3)/24 * P^2

 

Work is below

[Lara Hulbert]

My graph:

My analysis: 

[Lara Hulbert]

And some interesting spoiler alerts made by people who are not me:
http://blog.mrmeyer.com/wp-content/uploads/110927_1hi.png
http://scottfarrar.com/blah/perimeter_v_area.html