Squaring the Circle

[Bonzo]

A marble runs round a square.

Not really a puzzle, but how it works may be.

The ancients proposed a challenge - to construct a square with the same area as a given circle using only a straight edge and pair of compasses.
Some 4000 years later, in 1882 it was at last proved to be impossible "because of the transcendental nature of pi..."
Since, "Squaring the Circle" has come to mean, "Attempting the impossible".

[Rubenandres77]

Thanks for sharing!
It is a sweet little model.

Simple but very unusual and interesting

[SCEtoAUX]

Nice little model. Thanks for posting it.
I built another marble run a few years ago by John Boaz with a similar motor where the marble rolled along a spiral ramp then dropped and continued until the motor ran out. He called that one a Helix marble run.
Gonnahafta try this Squaring the Circle one also.

[Yale]

FWIW, Bonzo, squaring the circle was one of the three classical problems of ancient math, often known as quadrature. The others were trisecting an angle (trisection), and doubling the volume of a given cube (duplation). As you mention, late in the 19th century it was proven that all three problems are not solvable with classical tools -- an unruled straightedge and a "collapsing" compass. (That is, you could use the compass only to make arcs and circles, not for transferring a line length to another place.)
So don't worry -- even after your clever puzzle/toy, you needn't run out of challenges.

[Philip]

Just come across this. Thank you , Bonzo.

[Bonzo]

You can download a video of it running in "Download - Toys and automata - Squaring the circle"

[JohnGay]

As long as we're delving into mathematics here:
Recently someone at Google solved 33 = x^3 + y^3 + z^3
Also known as the sum of 3 cubes. Not to get too intricate, but the idea is to find 3 integers x, y, and z that when each cubed, and then added together equals another integer. Certain numbers are ruled out but a simple rule, but the rest "may" have an answer. And someone at Google just figured out that answer for 33.
Now the only number under 100 left to find is, Life, the universe and everything! 42.

[John Wagenseil]

https://www.quora.com/Does-equation-...eger-solutions

Originally Posted by JohnGay

As long as we're delving into mathematics here:
Recently someone at Google solved 33 = x^3 + y^3 + z^3
Also known as the sum of 3 cubes. Not to get too intricate, but the idea is to find 3 integers x, y, and z that when each cubed, and then added together equals another integer. Certain numbers are ruled out but a simple rule, but the rest "may" have an answer. And someone at Google just figured out that answer for 33.
Now the only number under 100 left to find is, Life, the universe and everything! 42.

They used negative integers to obtain the solution.