In arithmetic series, like 1 + 2 + 3 + 4 + 5 + … , each term differs from the previous one by a fixed amount. There is a formula for calculating the sum of the first N terms. For geometric series, like 3 + 6 + 12 + 24 + … , each term is a fixed multiple of the previous one. Again, there is a formula for the sum of the first N terms of such a series. Continue reading ‘Breaking Weather Records’
Archive for April, 2014
Tags: Geophysics, Number Theory, Probability
Tags: Euler, Geometry, Mechanics, modelling
The article in this week’s That’s Maths column in the Irish Times ( TM043 ) is about the mathematical curves called clothoids, used in the design of motorways.
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Tags: Applied Maths, Mechanics, Physics
We all know the feeling when a car takes a corner too fast and we are thrown outward by the centrifugal force. This effect is deliberately exploited, and accentuated, in designing rollercoasters: rapid twists and turns, surges and plunges thrill the willing riders.
Many modern rollercoasters have vertical loops that take the trains through 360 degree turns with the riders upside-down at the apex. These loops are never circular, for reasons we will explain.
Continue reading ‘Rollercoaster Loops’
This week, That’s Maths in The Irish Times ( TM042 ) is about the remarkable capacity of mathematics to anticipate physical phenomena that have not yet been observed.
The mathematical equations that express the laws of physics describe phenomena seen in the real world. But they also allow us to anticipate completely new phenomena.
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