Math
We summarize the week's scientific breakthroughs every Thursday.
- Math
A Geometric Superformula
The notion of a simple equation that you can use to generate a wide variety of geometric shapes is an immensely appealing one. Johan Gielis of Antwerp, Belgium, proposes one such formula in the March American Journal of Botany. “Many geometrical forms, both in nature and culture, can be interpreted as modified circles,” Gielis states. […]
- Math
Spheres in Disguise: Solid proof offered for famous conjecture
A Russian mathematician has proposed a proof of the Poincaré conjecture, a question about the shapes of three-dimensional spaces.
- Math
Recycling Topology
It’s hard to miss the triangle of three bent arrows that signifies recycling. It appears in newspapers and magazines and on bottles, envelopes, cardboard cartons, and other containers. The recycling symbol. Alternative (incorrect?) rendering of the recycling symbol. Cliff Long made a Möbius band the basis of his wood carving “Bug on a Band.” Photo […]
- Math
The Colors of an Equation’s Roots
Over the centuries, mathematicians have developed a variety of methods of solving equations. Using the capabilities of modern computers, they have explored in detail how these age-old recipes work–when the methods can be relied upon, when they fail, and when they behave strangely. A polynomiograph of a degree-36 polynomial. B. Kalantari “Cathedral” by B. Kalantari. […]
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- Math
Prime conjecture verified to new heights
Computations show that all even integers up to 4 x 1014 can be written as the sum of two prime numbers, lending support to the Goldbach conjecture.
- Math
Constructing Domino Portraits
In 1840, the Danish artist Christian Albrecht Jensen (1792–1870) was commissioned to paint a portrait of the renowned mathematician Carl Friedrich Gauss (1777–1855). This portrait, showing Gauss at the venerable age of 63, went on display at the Pulkowa Observatory in St. Petersburg, Russia, where it remains to this day. That painting of Gauss has […]
- Math
Zeroing In on Catalan’s Conjecture
Fermat’s last theorem is just one of many examples of innocent-looking problems that can long stymie even the most astute mathematicians. It took about 350 years to prove Fermat’s scribbled conjecture, for instance. Now, Preda Mihailescu of the Swiss Federal Institute of Technology in Zurich has proved a theorem that is likely to lead to […]
- Math
Zeroing In on Catalan’s Conjecture
Fermat’s last theorem is just one of many examples of innocent-looking problems that can long stymie even the most astute mathematicians. It took about 350 years to prove Fermat’s scribbled conjecture, for instance. Now, Preda Mihailescu of the Swiss Federal Institute of Technology in Zurich has proved a theorem that is likely to lead to […]
- Math
Zeroing In on Catalan’s Conjecture
Fermat’s last theorem is just one of many examples of innocent-looking problems that can long stymie even the most astute mathematicians. It took about 350 years to prove Fermat’s scribbled conjecture, for instance. Now, Preda Mihailescu of the Swiss Federal Institute of Technology in Zurich has proved a theorem that is likely to lead to […]
- Math
Zeroing In on Catalan’s Conjecture
Fermat’s last theorem is just one of many examples of innocent-looking problems that can long stymie even the most astute mathematicians. It took about 350 years to prove Fermat’s scribbled conjecture, for instance. Now, Preda Mihailescu of the Swiss Federal Institute of Technology in Zurich has proved a theorem that is likely to lead to […]
- Math
Square of the Hypotenuse
There’s a delightful mathematical moment in the movie Merry Andrew, when Danny Kaye, playing schoolmaster Andrew Larabee, breaks into song to teach the Pythagorean theorem. I was reminded of this scene by a sentence in an article about the Pythagorean theorem in the October issue of Mathematics Magazine. The Pythagorean theorem “is probably the only […]
