The authors of the recent Note [1] exhibit an odd preference. They derive recurrence relations for the odd terms, un = F2n+1, n ≥ 0, in the sequence of Fibonacci numbers, Fn, defined by

Illustrative examples which draw on everyday experience are particularly useful in the classroom. For this reason, sport can be a good source of examples. We present four illustrations of the ways that mathematics arises in different sports. The ideas should be understandable to those studying A-level mathematics.

The celebrated Steiner-Lehmus theorem states that if two internal bisectors of a triangle are equal then the triangle is isosceles. It beautifully illustrates the point that the converse of a theorem may be far more difficult to prove than the direct statement. The literature of the Steiner-Lehmus theorem is considerable with many contributions in the Mathematical Gazette.

An interesting variation on this theme may be found by examining the triangle formed by the second intersections of the medians with the circumcircle. Let the median point of a triangle ABC be G and let the medians meet the opposite sides at DEF and the circumcircle again at LMN.

The American Mathematical Monthly in Vol. 68 (1961) page 380 gave a solution by Leon Bankoff of the following problem proposed by A. Oppenheim of the University of Malaya in Vol. 67 (1960) page 802.