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Niles Johnson
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Inspired by +Kate Ponto, I made my own hyperbolic disks this weekend. I've seen these several times, but the construction is not particularly interesting (just keep increasing stitches!) and I didn't have a good reason to make them. But they are fun to handle, and it was a good project for a quiet afternoon.

I used a double-crochet for the one on the left, and it's a little more flexible than the standard (single-crochet) one on the right. I also learned how to crochet "in the round", which is what they call it when you make concentric rings of stitches instead of stacked rows.

Try an image search if you want to see the better ones that other people have made!


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This thing is amazing!
CIA Planimeter
via +Vicky Veritas

Surprisingly, it's possible to physically compute the area of an arbitrary two-dimensional shape, like a country on a map, simply by carefully tracing its perimeter with a suitable measuring instrument called a Planimeter.

The mathematics of the planimeter is supported by Green's Theorem named for the British Mathematical Physicist, George Green, whose other work underpinned the developments of James Clerk Maxwell and William Thomson by providing a mathematical model of electricity and magnetism.

Paul Kunkel says...

When I first used a planimeter, I was somewhat troubled by the fact that I did not understand how it worked. Oh sure, I don't understand how my car works either, but the planimeter essentially has only three moving parts. That makes its mechanism considerably less complex than a typical doorknob. After eighteen years of sleepless nights, I decided to buy a planimeter and figure it out.

More here:

Green's Theorem (Wikip):

George Green (Wikip):

There are several kinds of planimeters, but all operate in a similar way. The precise way in which they are constructed varies, with the main types of mechanical planimeter being polar, linear and Prytz or "hatchet" planimeters. The Swiss mathematician Jakob Amsler-Laffon built the first modern planimeter in 1854, the concept having been pioneered by Johann Martin Hermann in 1814. Many developments followed Amsler's famous planimeter, including electronic versions.

Planimeter (Wikip):

Image: from from
Rolling Disc Planimeter
Cartographers used this German-made device to accurately measure the size of an area on a map or plan by tracing the area’s outline. The area calculation used the resulting dial reading.


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Another great article from +Quanta Magazine. This one includes such gems as

In mathematics, it takes a community to read a paper.


... when you have a new subject, it’s difficult to figure out what is easy to see. (quoting Mohammed Abouzaid [1])

The early days of symplectic geometry — a field that begins with the movement of particles in space — were a bit like the start of a gold rush. But now that mathematicians have picked all its low-hanging fruits, they are left facing the shaky foundations.

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My plans for tomorrow, partly to support the march, but mostly because I want my son to see it.

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Indeed, this article was a lot more useful than I expected it to be. Time well-spent.
The long-read article below by the incomparable +Francis Su  makes a lot of wonderful and inspiring points, but hits out early with (among other things) a warning:

... we hear voices in the public sphere saying: “high school students don’t need geometry” or “let’s leave advanced math for the mathematicians”. And some mathematicians won’t admit it but they signal the exact same thing by refusing to teach lower-level math courses, or viewing the math major as a means to weed out those they don’t think are fit for graduate school.

I think it should be required reading for anyone learning mathematics, and anyone teaching mathematics. And a strong recommendation for most other people.

Via +David Butler  on Twitter

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Netflix Knows....
A fun psychological study about the power of visuals within your marketing. This is why you need a smart image.

#socialmediapsychology   #visualmarketing  

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Rollercoaster indeed!!
A lot has gone wrong recently, but at least one thing that went wrong has now been reversed, so in a small way (but not at all small for complexity theorists) the world is a good place again ...

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Ester Dalvit just released on YouTube a series of videos about knots in 4D. A realization of high quality and excellent explanations.

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What does 2017 look like? Here's a picture of the curve x^2 + y^4 = 2017, with the point (44,3) marked.

By the way, if you don't already know where people are getting these bizarre number facts, the OEIS is a good place to start. It's my first resource for number facts!
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