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. In fact, these four statements may or may not be true. For example, two parallel lines … Continue reading Bézout’s Theorem
Month: January 2014
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 … 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 … 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 … 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. According to the old adage, water finds its own level. But this is true only in static situations. In more dynamic circumstances where the water is moving rapidly, there can be … Continue reading Interesting Bores
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