A little while ago, I found a couple of books in a local used book store that I thought were pretty cool and that I thought I’d post little tidbits from, from time to time.
The first book is A Dictionary of Fabulous Beasts, by Richard Barber and Anne Riches. The second is Numbers, by David Wells.
Beast: Aigamuchas:
A creature which lived in the Kalahari desert with eyes on the top of its feet and thin pointed teeth as long as a man’s finger. If these creatures wanted to know what was happening behind them they went on hands and knees with one foot lifted so that they could see backwards. They hunted men as if they were zebras and ate them.
Number: 5.256946404860…
The approxximate ‘volumes’ of the unit radius ‘spheres’ in dimensions from 1 upwards are:
| dim.1 | dim.2 | dim.3 | dim.4 | dim.5 | dim.6 | dim.7 |
| 2 | 3.1 | 4.2 | 4.9 | 5.264 | 5.2 | 4.7 |
The volume is a maximum in 5 dimensions, and declines thereafter. If however the dimension is regarded as a real variable, able to take non-integral values, then the maximum volume occurs in ‘space’ of this dimension, 5.256… The volume is then 5.277768… compared to the volume in 5 dimensions of 5.263789… [David Singmaster]
(More information about n-spheres can be found here.)