Quick Snippets

Published on Thursday, March 28, 2013 in , , , , ,

Luc Viatour's plasma lamp pictureMarch's snippets may be a little late, but they are here!

This month, I present several classic geometry puzzles. Not all of them are solvable, but they are all interesting.

• Let's start this with one of the longest-running, and apparently most maddening, geometry puzzles in history! James Grime discusses “squaring the circle,” the challenge of constructing a square and a circle with the same area, using only a straight edge and a compass, in a finite number of steps:

Despite the impossibility, you can find many interesting approaches which have been tried over the years.

• One geometry puzzle that recently gained plenty of attention over at Gizmodo is the Winston Freer Tile Puzzle. You can purchase your own here, or a smaller version here, but ponder the seeming impossibility of it first:

James Tanton posted an interesting geometric challenge which can be presented in stages. The first challenge is just to determine the size of an arc without a protractor. This is usually solved by finding the center first, but can you do it without finding the center?

• Sometimes geometry itself is the puzzle! Jeff Dekofsky, via TedEd, discusses Euclid's puzzling parallel postulate. This is another part of geometry in which the answer will be forever closed off to us, but will remain interesting to ponder:

• I'll wrap March's snippets with Emma Rounds' poem, “Plane Geometry,” a parody of Lewis Carroll's classic “Jabberwocky”:

‘Twas Euclid, and the theorem pi
Did plane and solid in the text,
All parallel were the radii,
And the ang-gulls convex’d.

“Beware the Wentworth-Smith, my son,
And the Loci that vacillate;
Beware the Axiom, and shun
The faithless Postulate.”

He took his Waterman in hand;
Long time the proper proof he sought;
Then rested he by the XYZ
And sat awhile in thought.

And as in inverse thought he sat
A brilliant proof, in lines of flame,
All neat and trim, it came to him,
Tangenting as it came.

“AB, CD,” reflected he–
The Waterman went snicker-snack–
He Q.E.D.-ed, and, proud indeed,
He trapezoided back.

“And hast thou proved the 29th?
Come to my arms, my radius boy!
O good for you! O one point two!”
He rhombused in his joy.

‘Twas Euclid, and the theorem pi
Did plane and solid in the text;
All parallel were the radii,
And the ang-gulls convex’d.

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