Chapter 48: Mathematical Zoo

Chapter 48, Mathematical Zoo, is a particularly strange chapter. This chapter talks about the authors idea of "a zoo designed to display animals with features of special interest to recreational mathematicians". They go on to say that this type of zoo would be both entertaining and instructive. They say it would be divided in to two main wings one for living animals and the other for pictures, replicas, and animated cartoons of imaginary creatures. Many of these Imaginary creatures you would not think possible to exist however Gardner explains how they are not too farfetched. One of these beings is named A Wheeler, illustrated in figure 48.5. A Wheeler is an animal that has wheels instead of feet. Gardner quotes Robert G Rogers to help explain why the idea is not so insane. He quotes that if a wheel was "mounted on a bone bearing joint, with flexible veins and arteries, and a continuous series of circumferential pads(as on a dogs paw), the wheel could be wound back one turn by its internal muscles, then placed on the ground and rotated forward two full turns". If the wheel had a diameter of one foot this process would cause the Wheel to travel 6 and a quarter feet.

                Another organism Gardner would want in his zoo is a microscopic organism called radiolaria. These are one celled organisms that are found in the sea and have astonishing geometrical symmetries. Gardner cites an German biologist Ernst Haeckel who describes thousand of radiolaria in his Monograph of the Challenger Radiolaria. In this book there are 140 plates of drawings that display the geometric details of the different intricate forms of raiodlaria.

                Another portion of this chapter mentioned how the insect room at the zoo would display bees and there use of hexagonal honeycombs.  Scientists such as Darwin have marveled at bees use of honeycombs calling the ability to utilize them "the most wonderful of known instincts," and "absolutely perfect in economizing labor and wax.". While Gardner agrees that honeycombs are a great way of economizing wax he does state that there are better ways of doing it such as with a polyhedral cell.

                In  J. Diamonds "Why Animals Run On Legs, Not On Wheels," Diamond addresses the idea of why it is animals have legs instead of wheels. This article was actually very interesting. It talked about how bikes and other wheeled forms of transportation are actually more efficient than walking. So the question is why haven't animals evolved into having wheels instead of feet or legs. One thing that would have been nice to see in Gardner's Chapter 48 would have been the fact that wheels for feet would have made transportation for many animals near impossible. Such as with an ant, while their terrain looks relatively flat to us to an ant climbing the small hills would be near impossible. This bit of information would have been nice to see in the chapter because it shows the down side of having wheels instead of legs and how it is not optimal for all animals. One thing I was glad Gardner didn't include was the part where Diamond started talking about ancient civilizations. It isn't because this part was difficult to understand it was just the fact that it is irrelevant to the idea of a Zoo.

                In Jorge Luis Borges The Book of Imaginary beings Borges talks about many imaginary creatures, as you may have guessed by its title. This book in itself is interesting however much of it is irrelevant to mathematics. I'm glad Gardner did not include all of these beings due to many of them being irrelevant though I would have liked to see him include one named "The Leveler". This one resembles an elephant and has very wide flat feet. The leveler is supposedly 10 times larger than an elephant and would be used to level ground that was going to be built on. I think this would have been an interesting animal for Gardner to include in this chapter so he could have proved or disproved its ability to exist.

                L. F Toth "What Bees Know and What They Don't Know" is another one of the sources Gardner cites in his works. One thing I wish Gardner would have included was the formula Toth mentions in his work. In my opinion this would have helped to tie the honeycomb to mathematics. One thing I'm glad he included was why some scientists believe bees build the honeycombs in the shape they do. They believe it is less a result of evolution than an accidental product of how bees use their bodies.