Two lines in a plane intersect at one point, a line cuts a circle at two points, a cubic (an S-shaped curve) crosses the *x*-axis three times and two ellipses, one tall and one squat, intersect in four places.

## Archive for January, 2014

### Pythagorean triples

Published January 23, 2014 Occasional ClosedTags: Algorithms, Geometry, History

The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. It can be written as an equation,

*a ^{2 }+ b^{2} = c^{2},*

where *c* is the length of the hypotenuse, and *a* and *b* are the lengths of the other two sides.

### Robots & Biology

Published January 16, 2014 Irish Times ClosedTags: Applied Maths, Hamilton, Mechanics, modelling

The article in this week’s *That’s Maths* column in the* Irish Times* ( TM037 ) is about connections between robotics and biological systems via mechanics.

The application of mathematics in biology is a flourishing research field. Most living organisms are far too complex to be modelled in their entirety, but great progress is under way in simulating individual organs and modelling specific functions such as blood-flow and locomotion.

### White Holes in the Kitchen Sink

Published January 9, 2014 Occasional ClosedTags: Applied Maths, Fluid Dynamics, Mechanics, Physics, Wave Motion

A tidal bore is a wall of water about a metre high travelling rapidly upstream as the tide floods in. It occurs where the tidal range is large and the estuary is funnel-shaped (see previous post on this blog). The nearest river to Ireland where bores can be regularly seen is the Severn, where favourable conditions for these hydraulic jumps occur a few times each year.

But you do not have to leave home to observe hydraulic jumps. Continue reading ‘White Holes in the Kitchen Sink’

### Interesting Bores

Published January 2, 2014 Irish Times ClosedTags: Applied Maths, Fluid Dynamics, Geophysics, Mechanics, Wave Motion

This week’s *That’s Maths* column in the* Irish Times* ( TM036 ) is about bores. But don’t be put off: they are very interesting.