Category Archives: Beauty

An Einstein Ring

Source: New Scientist, Sep 2016

Lower right-hand corner depicting a blue circle surrounding a yellow dot

A Close-Up

Online Encyclopedia of Integer Sequences – Neil Sloane

Source: Quanta Magazine, Aug 2015

the Online Encyclopedia of Integer Sequences (OEIS), often simply called “Sloane” by its users.

This giant repository, which celebrated its 50th anniversary last year, contains more than a quarter of a million different sequences of numbers that arise in different mathematical contexts, such as the prime numbers (2, 3, 5, 7, 11 … ) or the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13 … ). What’s the greatest number of cake slices that can be made with n cuts? Look up sequence A000125 in the OEIS. How many chess positions can be created in n moves? That’s sequence A048987. The number of ways to arrange n circles in a plane, with only two crossing at any given point, is A250001. That sequence just joined the collection a few months ago. So far, only its first four terms are known; if you can figure out the fifth, Sloane will want to hear from you.

A mathematician whose research generates a sequence of numbers can turn to the OEIS to discover other contexts in which the sequence arises and any papers that discuss it. The repository has spawned countless mathematical discoveries and has been cited more than 4,000 times.

Are there other repositories of mathematical information that you wish existed, but don’t yet?

You would like an index to theorems, but it’s hard to imagine how that would work.

We’re trying to get a collaboration going with the Zentralblatt — the German equivalent of Math Reviews’ MathSciNet — about making it possible to search for formulas in the OEIS. Suppose you want the summation of xn over n2 + 3, where the sum goes from one to infinity. It’s very hard to look that up in the OEIS at present.

Poi Performance Art

 

Bull’s Eye (from Space)

Source: NASA, Mar 2008

This prominent circular feature in the Sahara desert of Mauritania has attracted attention since the earliest space missions because it forms a conspicuous bull’s-eye in the otherwise rather featureless expanse of the desert.

Described by some as looking like an outsized fossil in the desert, the structure, which has a diameter of almost 30 miles, has become a landmark for shuttle crews.

The World Visualized by Air Traffic

Source: Martin Grandjean website, Jun 2016

People travel not just more frequently, but increasingly far and quickly. Mapping the connections between all the airports worldwide is a fascinating network visualization exercise.

… an attempt to make explicit the network behind air transport.

 

Crochet of a Hyperbolic Structure

Source: The Institute for Figuring, Winter 2004

a physical model of the hyperbolic plane – a feat many mathematicians had believed was impossible – using, of all things, crochet. Taimina and her husband David Henderson, a geometer at Cornell, are the co-authors of “Experiencing Geometry,” a classic textbook on Euclidean and non-Euclidean space.

One way of understanding it is that it’s the geometric opposite of the sphere. On a sphere, the surface curves in on itself and is closed. A hyperbolic plane is a surface in which the space curves away from itself at every point.

One of the things that’s changing now is the advent of computers, which can help us to visualize mathematical objects.

Inspiration

Source: NYTimes, Apr 2016

… moments of inspiration don’t quite make sense by normal logic. They feel transcendent, uncontrollable and irresistible. When one is inspired, time disappears or alters its pace. The senses are amplified. There may be goose bumps or shivers down the spine, or a sense of being overawed by some beauty.

Inspiration is always more active than mere appreciation. There’s a thrilling feeling of elevation, a burst of energy, an awareness of enlarged possibilities. The person in the grip of inspiration has received, as if by magic, some new perception, some holistic understanding, along with the feeling that she is capable of more than she thought.

Inspired work stands apart from normal life. In the first place it’s not about self-interest as normally understood. It’s not driven by a desire for money or grades or status. The inspired person is driven intrinsically by the work itself. The work takes hold of a person.

Inspiration is not earned. Your investment of time and effort prepares you for inspiration, but inspiration is a gift that goes beyond anything you could have deserved.

It’s a beautiful contagion that passes through individuals. The word itself comes from the Latin inspirare, meaning “to breath into.” One inspiring achievement — say, the space program — has a tendency to raise the sense of possibility in others — say, a little boy who dreams of being an astronomer. Then the one who is inspired performs his own feats and inspires others, and so on down the line.

Most important, inspiration demands a certain posture, the sort of posture people feel when they are overawed by something large and mysterious. They are both humbled and self-confident, surrendering and also powerful. When people are inspired they are willing to take a daring lark toward something truly great. They’re brave enough to embrace the craggy fierceness of the truth and to try to express it in some new way.