Fractais e a Arte da Rugosidade

Isto é Matemática - Episódio 7

A Matemágica de Arthur Benjamin

Pinguins e Matemática

«Don't let the adorable mini-orchestra-conductor look fool you: penguins aren't that nice. When emperor penguins huddle together during Antarctic storms, they act like they're all in it together. But a new mathematical model shows just how the clusters of birds keep warm, accounting for everything from their geometry to the speed of the wind. Concern for one's fellow bird, it turns out, isn't a factor.

(...) 

To pack their penguin huddle as tightly as possible, the mathematicians imagined the birds on a grid of hexagons. This is the best way for circles to squeeze into a plane (think of a honeycomb), and scientists in the field have observed that real penguins arrange themselves roughly this way. The researchers also assumed that "penguins in this huddle have uniform size and shape."

Next, they added wind to the model, which flowed around the huddle differently depending on its overall shape. Then they calculated the rate at which each computerized penguin was losing body heat. They sent the coldest penguin shuffling around the outside of the huddle until it found the warmest spot it could stand in, then started over with the new coldest penguin.

The simulated penguins constantly shifted positions within the huddle, just as real penguins do. Over time, the model huddle tended to take on the shape of a flat-sided oval and travel slowly downwind (as penguins on the windward side continuously moved away from it).

When they calculated the flock's heat loss, the authors discovered that their model huddle was very fair: every penguin lost approximately the same amount of body heat. But these model penguins were only programmed to maximize their own warmth, not to consider the warmth of other penguins or the group as a whole. This means that even if penguins are only looking out for themselves, the whole huddle stays warm (...)»

Ler na íntegra aqui.

Isto é Matemática - Episódio 6

"The Unconscious Brain Can Do Math"

«In the second part of the study, the scientists examined how the unconscious brain processes math problems. Using the CFS technique again, the researchers subliminally exposed the participants to three-digit equations, such as "9 − 3 − 4," for two seconds or less. Then, the participants were shown a number (without CFS masking it) and told to say it out loud. The students were quicker to read aloud a number that was the right answer to the equation they had just subconsciously seen. For example, after being exposed to "9 − 3 − 4," they were quicker to pronounce "2" than "3." This suggests they subconsciously worked out the problem and had the answer on their lips. Other recent studies have shown that humans might be able to unconsciously perform tasks that have typically been associated with consciousness, such as learning and forming intuitions. The new study adds complex, rule-based operations to that list.»

Ler na íntegra aqui.

Isto é Matemática - Episódio 5

"¿Por qué los huracanes tienden a formar una espiral logarítmica?"

«Las espirales de los huracanes y de las tormentas tropicales se parecen bastante a una espiral logarítmica, aunque no lo son, y el ángulo a veces coincide con el de la espiral áurea, pero no siempre.»

Isto é Matemática - Episódio 4

Isto é Matemática - Episódio 3