but why would you graffiti the quadratic formula
some thugs just want to watch the world learn
(Source: cremitapalacara)
Spinning a cube along a diagonal gives an interesting shape, composed of two cones and a curved part whose cross-section is a hyperbolic curve. [more] [code]
Arranging 15 625 dots into a pattern. That is 5×5×5×5×5×5, so the dots can be arranged into pentagons within pentagons, going 6 levels down. This animation shows different amounts of spacing between the dots, revealing some interesting star patterns. [more] [code]
Bumblebees don’t need a map to know where they’re going. A large-scale experiment that outfitted the insects with radar antennas (shown) revealed that bumblebees are adept at figuring out the optimal route among several flowers, a tough computational problem. Credit: Andrew Martin
Bumblebees are anything but bumbling: The insects quickly figure out the optimal route for visiting five far-flung flowers, a computational task that even human brains find challenging.
That result suggests that an elaborate mental map isn’t necessary to travel efficiently in unknown territory. Finding a way to mimic the bumblebee’s navigation system may allow programmers to develop robots that adeptly maneuver through unfamiliar places.
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Fraud is one of the most serious concerns in science today. Every case of fraud undermines confidence amongst researchers and the public, threatens the careers of collaborators and students of the fraudster (who are usually entirely innocent), and can represent millions of dollars in wasted funds. And although it remains rare, there is concern that the problem may be getting worse.
But now some scientists are fighting back against fraud—using the methods of science itself. The basic idea is very simple. Real data collected by scientists in experiments and observations is noisy; there’s always random variation and measurement error, whether what’s being measured is the response of a cell to a particular gene, or the death rate in cancer patients on a new drug.
When fraudsters decide to make up data, or to modify real data in a fraudulent way, they often create data which is just “too good”—with less variation than would be seen in reality. Using statistical methods, a number of researchers have successfully caught data fabrication by detecting data which is less random than real results.
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You are about this far from the Sun.
Earth–Sun distance changes from slippery equation to single number.
Without fanfare, astronomers have redefined one of the most important distances in the Solar System. The astronomical unit (au) — the rough distance from the Earth to the Sun — has been transformed from a confusing calculation into a single number. The new standard, adopted in August by unanimous vote at the International Astronomical Union’s meeting in Beijing, China, is now 149,597,870,700 metres — no more, no less.
The effect on our planet’s inhabitants will be limited. The Earth will continue to twirl around the Sun, and in the Northern Hemisphere, autumn will soon arrive. But for astronomers, the change means more precise measurements and fewer headaches from explaining the au to their students.
The distance between the Earth and the Sun is one of the most long-standing values in astronomy. The first precise measurement was made in 1672 by the famed astronomer Giovanni Cassini, who observed Mars from Paris, France, while his colleague Jean Richer observed the planet from French Guiana in South America. Taking the parallax, or angular difference, between the two observations, the astronomers calculated the distance from Earth to Mars and used that to find the distance from the Earth to the Sun. Their answer was 140 million kilometres — not far off from today’s value.
Until the last half of the twentieth century, such parallax measurements were the only reliable way to derive distances in the Solar System, and so the au continued to be expressed as a combination of fundamental constants that could transform angular measurements into distance. Most recently, the au was defined as (take a deep breath): “the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of 0.01720209895 radians per day (known as the Gaussian constant)”.
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Japanese mathematician Shinichi Mochizuki claims to have found proof for the Abc Conjecture. If true, this means all prime numbers will be linked. The conjecture was proposed in 1985 and has remained unsolved until then.
Instead of explaining the conjecture myself, I’ll quote Yahoo! (if you’ll forgive me), as they had the simplest explanation:
The ABC conjecture makes a statement about pairs of numbers that have no prime factors in common, Peterson explained. If A and B are two such numbers and C is their sum, the ABC conjecture holds that the square-free part of the product A x B x C, denoted by sqp(ABC), divided by C is always greater than 0. Meanwhile, sqp(ABC) raised to any power greater than 1 and divided by C is always greater than 1.
I wouldn’t hold my breath waiting for confirmation, though. Shinichi Mochizuki’s proof is around 500 pages long.
A torus is shape defined as the shape formed by rotating a circle around an axis coplanar with the circle. The resulting shape will have one of three forms: a ring torus, in which the axis if revolution does not touch the circle; a horn torus, in which the circle is tangent to the axis; and a spindle torus, in which the axis is a chord of the circle. There are many real examples of the torus shape around the house: donuts, bundt cakes, life preservers, bicycle inner tubes and cushions.
The word torus is unchanged from Ancient Rome: the Latin word torus was a cushion. In architecture, the base of many columns contains a toroid, which acts as a ‘cushion’ for the column.
GIF of torus shapes courtesy Kieff who created the GIF and released it to the public domain. Thank you Kieff for such a beautiful image, and thank you for sharing your work with the world!
Image of The Column of Trajan, Rome, Dedicated in A.D. 113 to commemorate the emperor’s victory over the Dacians courtesy Roger Ulrich under a Creative Commons 3.0 license. Thank you Roger for releasing your word to Creative Commons.
This is THE original Woman In Math. The Big Math Momma. The Joan of Arcsines.
Born sometime between 350 and 371 AD in Alexandria, Egypt, Hypatia is the first notable woman in Western history to be known as a mathematician. Officially, she was Platonic scholar, the head of a school teaching peoples about Philosophy, Logic and Mathematics, for example.
She is thought to have to been a collaborator with her father (himself a famous mathematician) on most of her works. She published a well-read commentary on Diophantus’s Arithmatica, and another on Apollonius’s Conics.
However, she was widely believed to be the cause of strain between the Imperial Roman Prefect and the Patriarch Cyril, and because of that, attracted the hatred of the Christians of Alexandria, who wanted them to cease difficult relations. They jumped her on her way home, dragged her naked through the streets, and then killed her in the Caesareum Church, burning her remains after.
(Source: ihavenoidea28)
(Source: takemetobagend)