## Plus Blog

April 26, 2006
Wednesday, April 26, 2006
## 29 steps to universal (26/04/2006)Think of a number, any number, and see if you can write it as the sum of square numbers: In 1770, Lagrange proved that every positive integer, no matter how large, can be written as a sum of at most four squares, universal quadratic forms which could represent
all the positive integers. Another 53 expressions, including 1x, were found by Ramanujan in 1916. So many such universal forms exist, but how can you predict if a particular quadratic form is universal?^{2} + 2y^{2} + 3z^{2} + 5t^{2}Now the brilliant young mathematician Manjul Bhargava and his colleague Jonathan Hanke have found a surprisingly simple result that completely solves the problem of finding and understanding universal quadratic forms. They found a shortcut to deciding if a quadratic form is universal — to check if the form represents every single positive integer, you only have to check it represents a mere 29
particular integers, the largest of which is 290. Bharghava and Hanke then went on to find every universal quadratic form (with four variables), all 6,436 of them. You can read about this surprising result in Ivars Peterson's excellent article in Apart from Bhargava's brilliance as a mathematician (he was one of the youngest people to be made a full professor at just 28), he is also an accomplished musician. Both number theory and tabla playing may be viewed as the study of patterns, Bhargava told Peterson. "The goal of every number theorist and every tabla player," he explains in the article, "is to combine these patterns, carefully and creatively, so that they flow as a sequence of ideas, tell a story, and form a complete and beautiful piece." If you're struggling with a sum of squares, try out this useful applet by Dario Alpern.
## 0 Comments: |

March 29, 2006
Wednesday, March 29, 2006
## Frequently flipping fields (29/3/2006)In the past news story, Core business, we reported on research that the Earth's magnetic field may be in the early stages of a polarity reversal. These geomagnetic flips have occurred hundreds of times in the last 160 million years, and as the last one was 780,000 years ago many researchers think we are overdue for the next reversal. Until recently it was thought that the frequency of these polarity reversals was random, following a Poisson distribution. However Italian physicists have found that the process is better described by a Levy distribution — a distribution used for processes that exhibit "memory" of past events. So the pole reversals are not independent events, and this information should inform models of the magnetic dynamo process believed responsible. But as for when the next flip is due, that still remains a mystery. You can read about the strange magnetic fields of Uranus and Neptune in Untangling a magnetic mystery, and about the important role of the magnetic field in the Sun in The dynamic sun. You can also find out more about the Poisson distribution in On the ball.
## 0 Comments: |

March 14, 2006
Tuesday, March 14, 2006
## Happy Pi Day to you! (14/3/2006)Write the date March 14th in the date format used in the US and you get 3.14 — which makes it Pi Day! "If a billion decimals of pi were printed in ordinary type, they would stretch from New York City to the middle of Kansas. Only fortyseven decimal places of pi would be sufficiently precise to inscribe a circle around the visible universe that didn't deviate from perfect circularity by more than the distance across a
single proton."
## 0 Comments: |

February 16, 2006
Thursday, February 16, 2006
## Gravity kills dark energy? (16/02/2006)In 1998, scientists found that the rate at which the universe expands is accelerating. This was extremely puzzling, as none of the standard theories could account for the acceleration. So scientists decided that something unknown and mysterious must be responsible, and they called it You can find out more about the new model for gravity on Physicsweb, and more about dark energy in ## 0 Comments: |

January 27, 2006
Friday, January 27, 2006
## Small, cool planet found (27/01/2006)Scientists have found the smallest extrasolar planet yet. The inspiringly named OGLE-2005-BLG-390Lb orbits a red dwarf about 22,000 light years away, close to the centre of the Milky Way. Its mass is between 2.8 and 11 times that of the Earth's mass, possibly making it the least massive planet that has ever been found outside our own solar system. It's about 2.6 times as far away from its
star than the Earth is from the Sun. This distance, together with the fact that the star is a lot smaller and less bright than our Sun, means that temperatures on this icy, rocky planet are somewhere around -220° — too cold for life as we know it.
The planet was discovered using a new technique called Gravitational microlensing uses a different approach: as a star passes in front of a more distant reference object, its gravity acts like a lense and increases the object's brightness for a period of a few weeks. If the moving star has a companion planet, then this gives the brightness an extra spark. Although this is the third exoplanet discovered using gravitational microlensing, it's the first one of such low mass. Scientists think that these small worlds are much more common in the universe than was previously assumed. To find out more and see some pictures read this article from the European Southern Observatory.
## 0 Comments: |

January 25, 2006
Wednesday, January 25, 2006
## Football physics (25/01/2006)Nicholas Linthorne and David Everett from the University of Brunel, UK, have worked out the optimum angle for a footballer to launch a throw-in — it's 30 degrees to the horizontal, 15 degrees less than textbooks normally state. The two filmed a player throwing the ball at angles between 10 and 60 degrees and then used biomechanical software to measure velocity and angle in each case. Using the equations that describe the flight of a spherical object, they calculated the optimum launch angle to be 30 degrees. Thrown at this angle, the ball has the best chance to fly all the way to the penalty area, giving other players a great opportunity to score. And it goes even further if it's launched with a backspin at an even lower angle. The same methods can be used for any other sport involving the throwing of a ball. Next, Linthorne will calculate the optimum angle at which to take a goal kick. To find out more, read their paper Release angle for attaining maximum distance in the soccer throw-in, or look at Nicholas Linthorne's homepage.
## 0 Comments: |