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Flamingo. (1,6)-jumper.[All Comments] [Add Comment or Rating]

Charles Gilman wrote on Sat, Mar 29, 2003 08:49 AM UTC:

If there is no standard name for a 1:5 leaper I can suggest Zemel, and
while I am at it I can suggest Gimel for the 3:5 one. These names are
mathematically inspired.
	In the following all the variables are integers. If n can be expressed as
a²+b², then 2n=(b-a)²+(b+a)². If n is even so are b-a and b+a and both
sides can be divided by 4, making n/2 also a sum of squares. This means
that for every a:b leaper there is a (b-a):(b+a) leaper. Ignoring
non-coprime leapers this pairs leapers into a non-colourbound leaper with
an even and an odd component and a colourbound one with two odd
components. Such pairs are the 0:1 Wazir and 1:1 Fers, the 1:2 Knight and
1:3 Camel, the 2:3 Zebra and the 1:5, and the 1:4 Giraffe and the 3:5.
	Pronouncing the K in Knight gives 'Cannite', and the Knight has always
represented Cavalry, so '-mel' can be taken as an ending for a two-odds
leaper. Hence Zemel and Gimel.