Chapter 48: Mathematical Zoo

This chapter deals with an idea of creating a so called zoo that displays animals of interest to people. This so called zoo would be divided into two sections: one side with all the living creatures and the other with creatures that are imaginary. One room in the living section would contain microscopic animals such as the radiolaria, which are one-celled organisms in the sea. this creature can be described as spherical, with six claw-like extensions. one particular kind of radiolaria is the Aulonia Hexagonia. This sphere is covered with regular hexagons packed closely to each other. But there is a problem with this as it raised the question of whether it was possible to cover a sphere with hexagons. The correct answer is no and is explained with Euler's formula of F+C-E=2 where the letters stand for faces, corners, and edges. Someone did claim to have seen this kind of radiolaria even though it's not possible and it was clarified when if you zoom close enough, you see the shapes with less than six sides. Other examples include the many viruses that are shaped like icosahedra, a solid with three dimensions of triangular faces, and the twisted horns of certain sheep and goats.

Another section would contain animals that violate bilateral symmetry. Such examples are the Crossbill, a small red bird with its upper and lower beaks crossed. The aquarium of this zoo would have a tank full of male fiddler crab, which has either an enormous left or right claw. The flatfish is even weirder as it is bilaterally symmetric when they are young, but as they grow older, one eye moves over the top of its head to the other side. In a different tank, there would be a species of hagfish. This fish looks like an eel, has four hearts, and has teeth on its tongue. It's unique in that it can tie into a knot which is helpful to escape predators or to tear food from a large fish. The insect room would contain bees and wasps. Bees have a unique ability to create honeycomb nests that would use the least amount of wax and hold the most amount of honey inside. This is something that many people are shocked to know about bees and their amazing skill at this.

The Imaginary section of this zoo contains creatures that can only be thought of as fantasy. Some include the palindromic beasts, which have identical ends. An example of this is a palindrome dog, with heads at each end and legs. Imaginary creatures on wheels for transport would be another room in this section. Examples would be the Wheelers, a race of four-legged humanoids with wheels instead of legs and an Ork, a species of bird with propellers in the back that enable it to fly. In a different room, it would contain the Woozy. It is a block-headed, thick-skinned, dark blue creature with its body parts shaped like blocks. This beast behaves friendly unless a certain phrase is said which is "Krizzle-Kroo" in which it turns angry that causes its eyes to shoot fire. Another topic mentioned is the Buckyball. This carbon molecule is shaped spherically and resembles a soccer ball. The buckyball is the world's smallest atom shaped like a soccer ball that has 20 hexagon faces and 12 pentagons. This molecule was created my chemists in 1989 and belongs to a class of symmetrical molecules called fullerenes.

In Jarrod Diamond's article "Why Animals Run on Legs, Not On Wheels", he elaborates more on how animals haven't evolved to be able to have wheels to use to move around as opposed to human beings. It would have been good if Gardner included the three main reasons why animals are better off without wheels to show the other side of the argument. I'm glad he didn't include the history of how much we use these wheels for everyday life as it would distract from his main point on imaginary creatures with wheels.

In the article "Mathematics and the Buckyball" by Fan Chung and Shlomo Sternberg, it explains how this molecule drew interest from many different scientists in the many different areas of their expertise such as chemists, physicists, and chemical engineers. What made it so impressive was how it was symmetric that had various properties that can be explained with mathematics. It would have been good if Gardner included the different topics used to explain the buckyball and its properties. It was good that he didn't add in the complex mathematics involved with the buckyball as it would've confused the reader.

In the article "Great Balls of Fire" by Richard E. Smalley, he tells the background in creating the buckyball and the various methods used to make it work which eventually led to the creation of it. It would have been good if Gardner had added the moment when the chemists had succeeded in creating the buckyball. I'm glad he didn't add in the long process it took to create it has it would have made the reader less interested in the concept and would've been confusing to understand the details.

This chapter went into great detail on the various examples used in this mathematical zoo. It was interesting to read about the unique living creatures as well as some fantasy creatures that would be part of this so called zoo. Even though there were some topics that were hard to understand at first, rereading it made it easier for me to understand it better.