Bottema Article on Malfatti Problem

[Antreas P. Hatzipolakis]

Oene Bottema (1901-1992), the great Dutch geometer, published several
articles in the Dutch periodical _Euclides_. Among them is one on Malfatti
Problem:

O. Bottema: Verscheidenheden XXVI. Het vraagstuk van Malfatti.
Euclides 25 (1949-50), pp. 144-149. [in Dutch]

Jan P. Hogendijk kindly sent me a photocopy of the article, which I typed
and put in my web pages. Its URL is:

         http://users.hol.gr/~xpolakis/bottema/malfatti.html

Bottema generalizes Malfatti Problem, and gives interesting sequences
of circles. In these sequences appear two recursive integer sequences:

------

a(n): 0,16,160,1600,15840,....

a(1) = 0, a(2) = 16
a(2p+1) = 10a(2p) - a(2p-1)
a(2p) = 10a(2p-1) - a(2p-2) + 16

------

b(n): 2, 20, 198, 1960, .....

b(1) = 2, b(2) = 20
b(k) = 10b(k-1) - b(k-2)


Antreas