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! Plus is celebrating by reflecting on the ubiquitous usefulness of this number to mathematics, pondering its many unsolved mysteries, and
of course eating an appropriately shaped pi pie (pie are squared you know). How will you be celebrating? If reciting digits of pi is to be your pi party trick, then make sure you read Remembrance of numbers past from issue 31.
"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."
 from The Riciculously Enhanced Pi Page
posted by Plus @ 2:13 PM
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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 dark energy. But now three scientists claim that we may not need dark energy after all, but that the
acceleration can be explained by a modified model of gravity. They altered the equations from the theory of general relativity in a way prescribed by cosmological theories based on a universe with more than four dimensions. When applied to short distances (on the cosmological scale), the differences between the old and new models are not noticeable, however, on ultra large distances the new
equations predict the accelerated expansion. Moreover, the researchers say, the predictions match observations extremely well and don't conflict with other observations.
You can find out more about the new model for gravity on Physicsweb, and more about dark energy in Plus article New light shed on dark energy.
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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 OGLE2005BLG390Lb 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. Until now, planets were spotted by the way their gravitational pull makes their host star wobble, a technique which uses the Doppler effect (see Plus article Brave young worlds). But for this to work, the planet has to be massive
enough or close enough to its star to exert the necessary pull. Consequently, all planets found so far are much more massive than OGLE2005BLG390Lb.
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.
posted by Plus @ 2:11 PM
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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 throwin — 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 throwin, or look at Nicholas Linthorne's homepage.
posted by Plus @ 2:10 PM
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January 16, 2006
Monday, January 16, 2006
US law is Euclidean (16/01/2006)
This is what one James Robbins found out when he stood trial for drug dealing in New York last year. US law decrees that selling drugs within 1000 feet of a school carries extra penalties. Unfortunately, Robbins had been caught within that radius, so his lawyer decided simply to change the metric. He argued that the Euclidean metric, which measures distances along straight lines between
points, should be replaced by a "Taxicab metric", which measures distances along the roads a taxi, or a pedestrian, has to take to get from point to point. After all, students from the school in question are unlikely to walk through brick walls. According to this new metric, Robbins was 1254 feet away from the school: 764 feet north along Eighth Avenue and 490 feet west along 43rd Street. Alas,
judge and jury were unimpressed by this mathematical trickery and Robbins lost.
posted by Plus @ 2:09 PM
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January 16, 2006
Monday, January 16, 2006
Einstein is proved right (16/01/2006)
Unlike human celebrities, equations have to prove their merit to be famous. Now Einstein's e=mc^{2} has done just that. An experiment conducted by US researchers from the National Institute of Standards and Technology and the Massachusetts Institute of Technology, showed that e differs from mc^{2} by at most 0.0000004, proving beyond doubt that the equation
is indeed correct.
The equation, which just celebrated its 100th birthday, is part of Einstein's special theory of relativity and relates energy (e) to mass (m) and the speed of light (c). The recent experiment is the most precise and direct test of the equation ever conducted. Its results were published in the journal Nature. You can find out more about the experiment in this news release. To see special relativity in action, read Plus article What's so special about special relativity?. Another Plus article, Spinning in space, describes how the general theory of relativity is put to the
test.
posted by Plus @ 1:20 PM
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