July 13th, 2013| Topic: RaMbLeS | 0


Ever thought of the existence of square wheels? That would be the ultimate flat tire. And they would give you a pretty jarring ride on your usual flat road, if you put a couple of those wheels on your bicycle.

But apparently a mathematician—yes, a mathematician!—has created a bicycle (actually a tricycle) with square wheels. And, it gives a perfectly smooth ride.

Provided you ride it on a special road.

This trike with square wheels rolls quite smoothly, keeping its axle moving in a straight line and at constant velocity, as it negotiates those evenly spaced bumps created in a precise shape—an “inverted catenary” (aka a “hanging chain”). There is some complex math going on here, dealing with hyperbolic cosines (cosh x), none of which I claim to comprehend.

(My knowledge of matters technical is limited to esoteric concepts like lichen sclerosus et atrophicus and Naegeli–Franceschetti–Jadassohn syndrome, etc. No cosines, hyperobolic or otherwise, for me!)

So what you need for a road to ride your square-wheeled bike is a bed of inverted catenaries. (But don’t expect one in your neighborhood any time soon.)

Needless to say, steering is virtually impossible!

And, apparently, it’s not just square wheels that work this way. Any regular polygon can serve as a wheel … provided you have the right-shaped road (As the number of the polygon’s sides increases, the segments get shorter and flatter. And, ultimately, for a wheel with an infinite number of sides (which is in effect, a circle), the curve becomes a straight, horizontal line. Fascinating!

Triangles, however, don’t work. But rosettes, and ellipses, and teardrops, work quite well, as potential wheel shapes. Who knew?

Apparently the ancient Egyptians did. There has been some speculation about various pieces of wood cut in the shape of quarter circles (close enough to a catenary) that were discovered near the Pyramids. He thinks these formed a road that enabled construction workers to roll square-cut, multi-ton chunks of marble or stone easily.

Not all of us are circle-shaped. Some of us have odd shapes. In fact, no one is perfect. We all have weird idiosyncrasies and bumps and inconvenient corners. Not everyone has a smooth ride in this flat world. Some of us need special roads to negotiate life.

Sin, of course, has done its bit to cause us to be misshapen.

There is none righteous, not even one;
there is none who understands, there is none who seeks for God;
all have turned aside, together they have become useless;
there is none who does good, there is not even one.
Romans 3:10–12

Nope, not even one. No circles. Just a bunch of squares, hexagons, heptagons, octagons, nonagons, decagons, hendecagons, dodecagons, ….

Rough, rugged, ridged, and rutted.

All of us like sheep have gone astray,
Each of us has turned to his own way.
Isaiah 53:6a

But one took the fall for us.

But the LORD has caused the iniquity of us all
To fall on Him.
Isaiah 53:6b

Our Lord Jesus Christ. To straighten us all out. To perfect our circles.

Not that we are all rounded out now. For that we wait. Till we get to a place that has the perfect roads for each of us. Then the ride will be a roll! Smooth sailing. For ever.

And He will wipe away every tear from their eyes;
and there will no longer be any death;
there will no longer be any mourning, or crying, or pain.
Revelation 21:4

The perfect road is coming. Soon and very soon!



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