From the complexity of the snowflake, to the London tube map and the spiralling Andromeda galaxy, imagery has always been a vitally important ingredient of science. Plus talks to John Barrow, professor of mathematics at Cambridge University and author of the new book Cosmic Imagery, about the images that have changed science, and how we have viewed science, over the
This podcast is also available in an enhanced version, which shows all the images mentioned in this podcast as you listen. You can view the enhanced podcast in your browser, or download the MP4 file to to your computer and for playing on your MP4 player (for example iPod).
It is common belief among teachers and parents that when teaching mathematical concepts, the best way to illustrate them is with 'real-world' examples. However, researchers at Ohio State University's Center for Cognitive Science have found the exact opposite — that college students taught a new mathematical concept with real-world, concrete examples
were less able to apply their knowledge to new situations than students taught with abstract symbols.
There are more grains of sand on Earth than there are stars in sky, or so the saying goes.
Mathematician Anne Fey, from Vrije Universiteit Amsterdam, is using sand-pile models as a novel approach to calculate probabilities in fields as diverse as studies of the Earth's crust, stock market fluctuations and the formation of traffic jams.
Life is good for only two things, both mathematical
Siméon-Denis Poisson (born 21 June 1781 Pithiviers, France; died 25 April 1840 Sceaux, France) was a French mathematician and physicist who once stated:
"Life is good for only two things, discovering mathematics and teaching mathematics."
Poisson was a student of Laplace and Lagrange and achieved highly at a young age, writing a memoir on finite differences at 18 and graduating at 19 without needing to take the final examination. He then moved immediately to the position of
repetiteur at Ecole Polytechnique, which was quite an achievement as most top mathematicians had to serve in the provinces before getting a post in Paris.
In 1802, Poisson was named deputy professor and in 1806 he was appointed to the professorship that had been vacated by none other than Fourier. During this period, he studied ordinary and partial differential equations, and in particular their application to physical problems such as the pendulum and the theory of sound.
In 1808, Poisson became an astronomer at Bureau des Longitudes and in 1809 he added the chair of mechanics in Faculte des Sciences to his impressive list of appointments. In 1808 and 1809 Poisson published three important papers, the first investigating mathematical problems raised by Laplace and Lagrange about perturbations of
the planets, and the others incorporating developments in Lagrange's method of variation of arbitrary constants which had been inspired by the first of Poisson's three papers. In addition, he published a new edition of Clairaut's Theorie de la figure de la terre, which
had first been published in 1743 and confirmed the Newton-Huygens belief that the Earth was flattened at the poles.
In 1811, Poisson won a "Grand Prix" on electricity studies and in 1813 his results regarding the potential in the interior of attracting masses found application in electrostatics. Papers followed on the velocity of sound in gasses, on the propagation of heat, and on elastic vibrations.
It was in his 1837 work Recherches sur la probabilite des jugements en matière criminelle et matière civile that the Poisson probability distribution first appears. This distribution describes the probability that a random event will occur in a time interval when the probability of the
event occurring is very small and the number of trials very large.
Contrary to recent press reports, NASA offices involved in near-Earth object research were not contacted and have had no correspondence with a young German student, who claims the Apophis impact probability is far higher than the current estimate.
This student's conclusion reportedly is based on the possibility of a collision with an artificial satellite during the asteroid's close approach in April 2029. However, the asteroid will not pass near the main belt of geosynchronous satellites in 2029, and the chance of a collision with a satellite is exceedingly remote.
Therefore, consideration of this satellite collision scenario does not affect the current impact probability estimate for Apophis, which remains at 1 in 45,000.