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Non-Euclidean Geometry and Map-Making

Non-Euclidean Geometry and Map-Making | Science News | Scoop.it

One consequence of the fundamental difference between flat surfaces and spherical surfaces, such as the Earth, is that any planar depiction of the Earth – such as a map on the wall, in an atlas, or on Google Maps – will necessarily have some distortions.


Morehttp://www.science4all.org/scottmckinney/non-euclidean-geometry-and-map-making/

Sakis Koukouvis's insight:

The impossibility of making perfect maps

Ashley Willis's curator insight, March 30, 2015 11:41 AM

Very fun side topic for an advanced geometry class!

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[VIDEO] Hockey Geometry

[VIDEO] Hockey Geometry | Science News | Scoop.it

From the passes NHL players make to their teammates, to the shots they take to score, players in every position are constantly using geometry when playing the game. The lines, angles and curves on the ice are also examined. "Science of NHL Hockey" is a 10-part video series produced in partnership with NBC Learn and the National Hockey League.

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This planet obeys the law—stats on volcanic eruptions show pattern called Benford's Law

This planet obeys the law—stats on volcanic eruptions show pattern called Benford's Law | Science News | Scoop.it

Choose a number at random from scientific data. Think it's just as likely that it will start with a 9 as a 1? In many cases, you'd be wrong. The ages of volcanic calderas are one of those cases. Law-abiding citizens everywhere will be happy to know our planet also obeys Benford's Law, with the duration and size of volcanic eruptions showing the same sort of pattern.

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Spitzer finds solid buckyballs in space

Spitzer finds solid buckyballs in space | Science News | Scoop.it
(PhysOrg.com) -- Astronomers using data from NASA's Spitzer Space Telescope have, for the first time, discovered buckyballs in a solid form in space.
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Honeycomb structure responsible for bacteria's extraordinary sense

Honeycomb structure responsible for bacteria's extraordinary sense | Science News | Scoop.it
(PhysOrg.com) -- Cornell researchers have peered into the complex molecular network of receptors that give one-celled organisms like bacteria the ability to sense their environment and respond to chemical changes as small as 1 part in 1,000.
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Orbit Fractals

Orbit Fractals | Science News | Scoop.it
The only orbit plotted fractals (orbit fractals for short) I've dealt with so far are Pickover Popcorn fractals. For the next release of Saturn & Titan I decided to try plotting the orbits of a...
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How do snowflakes get their shape?

How do snowflakes get their shape? | Science News | Scoop.it
Depending on the temperature and humidity of the air where the snowflakes form, the resulting ice crystals will grow into a myriad of different shapes.
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Leonardo da Vinci's tree rule may be explained by wind

Leonardo da Vinci's tree rule may be explained by wind | Science News | Scoop.it
More than 500 years ago, Leonardo da Vinci observed a particular relationship between the size of a tree’s trunk and the size of its branches. Specifically, the combined cross-sectional areas of a tree’s daughter branches are equal to the cross-sectional area of the mother branch. However, da Vinci didn’t know why tree branching followed this rule, and few explanations have been proposed since then. But now in a new study, physicist Christophe Eloy from Aix-Marseille University in Aix-en-Provence, France, has shown that this tree structure may be optimal for enabling trees to resist wind-induced stresses.
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The Beauty of Roots

The Beauty of Roots | Science News | Scoop.it

Back in 2006, Dan Christensen did something rather simple and got a surprisingly complex and interesting result. He took a whole bunch of polynomials with integer coefficients and drew their roots as points on the complex plane. The patterns were astounding!

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Researchers link patterns seen in spider silk, melodies

Researchers link patterns seen in spider silk, melodies | Science News | Scoop.it
Using a new mathematical methodology, researchers at MIT have created a scientifically rigorous analogy that shows the similarities between the physical structure of spider silk and the sonic structure of a melody, proving that the structure of each...
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Leonardo’s Formula Explains Why Trees Don’t Splinter

Leonardo’s Formula Explains Why Trees Don’t Splinter | Science News | Scoop.it
Trees almost always grow so that the total thickness of their branches at a particular height is equal to the thickness of their trunks. Until now, no one has been able to explain why trees obey this rule, which Leonardo da Vinci first noticed.
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Snowflakes Under an Electron Microscope

Snowflakes Under an Electron Microscope | Science News | Scoop.it

Image: Electron and Confocal Microscopy Laboratory, Agricultural Research Service, U. S. Department of Agriculture. See Also: Strange Triangular

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[VIDEO] Proof Without Words: The Circle

Prove Ď€R⊃2; using only beads and a ruler!

I first saw this proof in an article by Russell Jay Hendel, Dowling College: http://bit.ly/LQlwQw

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Brain may not be hard wired to link numbers and space

Brain may not be hard wired to link numbers and space | Science News | Scoop.it
Our ability to map numbers onto a physical space – such as along a line – must be learned...


Articles about NUMBERS: http://www.scoop.it/t/science-news?tag=numbers



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5 and Penrose Tiling - Numberphile

Why five-sided figures pose a problem from Professor John Hunton - and a bit about the importance of Penrose Tiling. Professor Hunton works at the University...
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Desert Ants Are Better Than Most High School Students At Trigonometry

Desert Ants Are Better Than Most High School Students At Trigonometry | Science News | Scoop.it

Via Ale
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Testosterone, digit ratio, and abstract reasoning ability

Testosterone, digit ratio, and abstract reasoning ability | Science News | Scoop.it

We measure a digit ratio, abstract reasoning ability with the Raven Progressive Matrices task, and risk attitude with choice among lotteries. Low digit ratio in men is associated with higher risk taking and higher scores in abstract reasoning ability when a combined measure of risk aversion over different tasks is used.

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The Beautiful Math Of Coral

The Beautiful Math Of Coral | Science News | Scoop.it

Margaret Wertheim leads a project to re-create the creatures of the coral reefs using a crochet technique invented by a mathematician — celebrating the amazements of the reef, and deep-diving into the hyperbolic geometry underlying coral creation.

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Solar energy: New sunflower-inspired pattern increases concentrated solar efficiency

Solar energy: New sunflower-inspired pattern increases concentrated solar efficiency | Science News | Scoop.it
A new sunflower-inspired pattern increases concentrated solar efficiency.
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The Golden Ratio/Divine Code

The Golden Ratio/Divine Code | Science News | Scoop.it

There is a code that lies both within and without. This secret yet open code points the way to your purpose, your happiness and your greatness… it goes by the name of The Golden Ratio/Divine Code.


Via ramblejamble
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Quantum geometry

Quantum geometry | Science News | Scoop.it

Out of all these new ideas there is one that perhaps defies intuition more than all others: that space, when you zoom in on it, stops being a smooth and continuous whole and starts breaking up into little indivisible chunks of some kind. This idea is truly mind-boggling. When you think of little chunks you can't help but think of them as existing inside something else and this something is — well, continuous. Another visualisation is to imagine space becoming fuzzy at this fundamental scale. But what exactly does that mean? Fuzzy with respect to what? Our macroscopic intuition simply isn't equipped to deal with a non-continuous space. Maths is the only language in which to talk about this, but ordinary geometry won't do — we need a completely new model of space. Shahn Majid from Queen Mary, University of London, has developed such a model, based on something called non-commutative geometry. His work is a fascinating blend of abstract algebra, theoretical physics, philosophy and experiment. Plus went to see him to find out more.

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How to Turn a Sphere Inside Out

will blow your mind...
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Why solar wind is rhombic-shaped?

Why solar wind is rhombic-shaped? | Science News | Scoop.it
Why the temperatures in the solar wind are almost the same in certain directions, and why different energy densities are practically identical, was until now not clear.
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