Archive for January, 2014

Bézout’s Theorem

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.

Bezout-01 Continue reading ‘Bézout’s Theorem’

Pythagorean triples

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,

a2 + b2 = c2,

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

Continue reading ‘Pythagorean triples’

Robots & Biology

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.

Continue reading ‘Robots & Biology’

White Holes in the Kitchen Sink

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

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.

Continue reading ‘Interesting Bores’

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