Escher ]]>

I downloaded TED on Xbox one so re-blogging them is a must, they see life so unconventionally. ]]>

Continually subdivide a straight line into equal segments which eventually are so small they seem invisible. But since they still exist on that original straight line they collectively reconstitute it. The process can’t be said to have reduced the length of the line to 0. Same analysis applies to the attempt to subdivide the triangle in Riddle #1 to reduce its area to 0.

Create a circle of any circumference. Draw any number of radii in the circle. Join the points of the arcs they determine with straight lines to form a polygon which is enclosed entirely within the circle. Continue the process until the arcs become smaller and smaller and the number of sides of the polygon larger and larger suggesting its perimeter must be infinite. But that prospect is unattainable since the resulting polygon of however many sides remains bounded by the circle and its perimeter consequently can’t exceed the circumference originally chosen for the circle. The proposed solution to Riddle #2 represents the same notion. Creating the same false impression by instead forming polygons from the sides of a triangle. Hereto the perimeter of the polygon can’t exceed the circumference of a circle circumscribing the triangle.

May even seem reasonable to argue the TED solutions to Riddles #1 and #2 are contradictory. Residuals of subdivision are zero and infinite. Not even in a Noir World. Just feels that way.

]]>What fun! Elmo teaches math in dark, animated short! ]]>