Math Behind the Characteristic Shape of a Long Leaf Revealed

ScienceDaily (Nov. 26, 2009) — Applied mathematicians dissected the morphology of the plantain lily (Hosta lancifolia), a characteristic long leaf with a saddle-like arc midsection and closely packed ripples along the edges. The simple cause of the lily's fan-like shape -- elastic relaxation resulting from bending during differential growth -- was revealed by using an equally simple technique, stretching foam ribbons.

"These blades have rippled edges when they grow in slowly moving water. When they are transplanted to environments that have rapidly moving water, they generate new blades which are much narrower," says Mahadevan. "This example of phenotypic plasticity, or the ability of the algae to change their shape in response to environmental forces, led to a paper co-authored with Koehl and Silk last year that focused primarily on the experimental findings."

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Eureka! A Theater Play About Math?

When Marshfield math teacher Jean Kelley suggested last year that her friend Spring Sirkin produce a play about mathematics, Sirkin was skeptical.

“I didn’t think math concepts would naturally lend themselves to dramatic situations,’’ said Sirkin, whose Boston-based Chamber Theatre Productions tours the country with plays that support middle and high school instruction.

“We’ve always focused on the literature curriculum,’’ Sirkin said. “But we constantly ask teachers for feedback on what they’re reading and what they need help with. We were looking for something a little different, and when we polled teachers across the country, they overwhelmingly asked for a math play.’’

With Kelley as her consultant, Sirkin put out a call last spring to several play wrights to see what they might come up with. “Eureka!’’ by Shaun Wainwright-Branigan, jumped out at her right away.

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(Image credit: 10best.com)

Heads or tails? It all depends on some key - but unknown - variables

Physorg - Everyone knows the flip of a coin is a 50-50 proposition. Only it's not. You can beat the odds. So says a three-person team of Stanford and UC-Santa Cruz researchers. They produced a provocative study that turns conventional wisdom, well, on its head for anyone who has ever settled a minor dispute with a simple coin toss.

It also could have profound implications in America's favorite sport -- pro football -- because the coin flip plays an integral role in deciding games that go into overtime.

But first, here's what the researchers concluded: Using a high-speed camera that photographed people flipping coins, the three researchers determined that a coin is more likely to land facing the same side on which it started. If tails is facing up when the coin is perched on your thumb, it is more likely to land tails up.

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(Image credit: gazette.uwo.ca)

A Fraction of History

- An extensive treatment of fractions appeared around 1600 B.C. in the Rhind Papyrus, which contained the work of Egyptians mathematicians.

The Egyptians did not express fractions as ratios such as 2:5 or 2/5.

They expressed ratios in unit fractions.

Egyptians used their symbols to represent this fraction.
1/3 + 1/15 would be represented as shown below:

Notice that all we care about is the man's feet. Feet pointing toward the direction of writing means add. Otherwise, it means subtract...

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