Divina Commedia: Online at Columbia University.
If you think poetry and maths are poles apart, think again. Around the sixth century, Indian poet and mathematician Virahanka codified the structure of Sanskrit poetry, formulating rules for the patterns of long and short syllables. In this process, a sequence emerged in which each term is the sum of the preceding two. This is precisely the sequence studied centuries later by Leonardo Bonacci of Pisa, which we now call the Fibonacci sequence [TM241 or search for “thatsmaths” at irishtimes.com].
and 
. There is no point on the real line corresponding to the “North Pole” in 
in the plane 
and the sphere 
in three-space 
, we can consider hyper-spheres in higher dimensional spaces. In particular, we will consider the 3-sphere which can be embedded in 
but can also be envisaged as a non-Euclidean manifold in 
.
, Greek for hand. If chirality is absent, we have an achiral object.
and 
having the same underlying set 
but different families of open sets, a function may be continuous in one but discontinuous in the other.
![Solution of Steiner 5-point problem with soap film [from Courant and Robbins].](https://thatsmaths.files.wordpress.com/2015/01/steiner-5point.jpg)
![From left to right: Figure-of-8 knot 4_1, knot 6_3 , knot 7_1, and knot 8_5 [Fig from Van Wijk (2006)].](https://thatsmaths.files.wordpress.com/2015/01/knots-vanwijk.jpg)
together with a metric
follows from the metric.
ThatsMaths 