In honor of Hans Rosling

All of us must die.  Hans Rosling, who created a  representational language to depict a large variety of data, left the world yesterday. This post is in his honor. If you have never visited the website, there is a lot to explore, and many of the graphs give a clear and sometimes startling view of the world. Respresentation as a source of beauty.

Source: How Does Income Relate to Life Expectancy? – Gapminder

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Beautiful Math – National Museum of Mathematics

The Museum of Mathematics: Inspiring math exploration and discovery

Source: Beautiful Math – National Museum of Mathematics

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Mapping the world

Even in the task of making a 3D globe into a 2D map one can be guided by aesthetics.  Source: http://www.vox.com/world/2016/12/2/13817712/map-projection-mercator-globe

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Celtic Knot – A nice little pattern that uses rotational symmetry.

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Fibonacci in nature

From: https://edex.adobe.com/resource/2d35bc/

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Go’kväll takes on beauty in mathematics!

This week I had the honor of being on Go’kväll, a national Swedish tv program, to talk about  beauty in mathematics. How cool is it that the program has started to take on topics in mathematics and science:  Very cool.  We discussed what kind of example to give to give viewers a sense of what beauty in mathematics is like. In the end, even though we had simpler examples, we went with the one that really turned me on to mathematics.  It is an argument, formulated by Goerg Cantor in the late 1800s, which shows that there are different orders (sizes) of infinity.  Some sets of numbers, like counting numbers (1, 2, 3, 4… ) and rational numbers (including 1/2, 3/18, 9/49) can be shown to have the same size.  There is a clever way or ordering the rational numbers when you count them.  But if you try to do the same with real numbers (which includes irrational numbers like π and e, and all the rational numbers) you simply can’t do it.  The way to show this is to make a list of all the real numbers, as if you could do it. Just write them all down, doesn’t matter in what order, but make sure you have got them all.  Once you finish the list, which is supposed to have all the numbers, you can still construct another number that is not on the list!  You do it by writing down a number that differs in the first decimal place of the first number, in the second decimal place of the second number, etc.

Here is a link to the show:  GoKvall

For more info on Fibonacci numbers: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

 

 

 

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Månadens problem | NCM:s och Nämnarens webbplats

Problem of the month!  If you have children who are bored in your class, maybe they would be interested in this?

Source: Månadens problem | NCM:s och Nämnarens webbplats

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