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CIA Planimeter
via

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.

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More here: https://goo.gl/QaHZpB

Green's Theorem (Wikip): https://goo.gl/rO6T1z

George Green (Wikip): https://goo.gl/NSW3zZ

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.

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Planimeter (Wikip): https://goo.gl/p4FxMl

Image: https://goo.gl/DzjZqF from https://goo.gl/R7Gk0w from https://goo.gl/dgJr8P
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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Tie Knots

During their time at Cambridge University’s Cavendish Laboratory, Anglo-American Physicist Thomas Fink and his colleague Yong Mao learnt how to tie ties.

Seeking a marriage of science and beauty, Thomas M. A. Fink and Yong Mao, research fellows at Cambridge University, have applied the rigors of mathematics to that most basic of fashion statements, the necktie knot. In the process they have come up with six new ways of tying a tie.

Dr. Fink, who in his more serious moments investigates protein folding, and Dr. Mao, who specializes in colloids and polymers, felt that the world might be ready for a new knot or two. Of the four in common use, the four-in-hand (so named because it was used by drivers of four-in-hand carriages) dates from the 19th century, while the Windsor and the half-Windsor, were popularized in the 1930's by the Duke of Windsor. Only the Pratt knot, publicized about a decade ago, has a more recent history, and some dismiss it as simply a reverse Windsor.

More here (article): https://goo.gl/TKEHYR

Of the 85 possible tie knots that can be tied with a tie of conventional length, the following are of particular interest. The first number is the number of the knot, as catalogued in the Summary of Knots in The 85 Ways and at the bottom of this page. Some of the knots have close cousins with which they are often confused (not including mirror images). These typically involve the transposition of one or more L-R pairs. They are indicated by prefixing the name of their relation with 'co-', as in co-Windsor.

More here (blog): https://goo.gl/ahS7N7

The discovery of all possible ways to tie a tie depends on a mathematical formulation of the act of tying a tie. In their papers (which are technical) and book (which is for a lay audience, apart from an appendix), the authors show that necktie knots are equivalent to persistent random walks on a triangular lattice, with some constraints on how the walks begin and end. Thus enumerating tie knots of n moves is equivalent to enumerating walks of n steps. Imposing the conditions of symmetry and balance reduces the 85 knots to 13 aesthetic ones.

The 85 Ways to Tie a Tie (Wikip): https://goo.gl/Pr3y4Y

The 85 Ways to Tie a Tie (Library): https://goo.gl/vz8SCm

Designing tie knots by random walks (Nature pdf): https://goo.gl/IFXr0z

Tie knots, random walks and topology (Nature pdf): https://goo.gl/pnHcZW

Image: https://goo.gl/HBxrJe
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Karlie Noon

Despite obstacles from her background, twenty-six year-old Karlie Noon just graduated from the University of Newcastle in Australia with a degree in Pure Maths and Physics, thanks to her hard work, a turning point and a mentor.

Karlie Noon: I didn't go to school much. I think most of the time my attendance was below 50%. I really disliked school. We were really poor growing up as well. My mum has quite a few disabilities, and so she was on the disability pension, so that was the wage that we lived off. My clothes were always dirty, I was always smelly, I never had food or money. I guess I got picked on a lot.

Anna Salleh: But help was at hand, and Karlie ended up excelling in maths.

Karlie Noon: We had this family friend who was a local elder in the community, a really good friend of my grandma, and she would come over every week and she would tutor me in maths. And so I had this inspiration in my life from a really young age, and also the support, and so maths was by far my strongest subject.

More here (interview transcript): https://goo.gl/6m938p
(The transcript hashtag in the URL doesn't work properly.)

Karlie tosses her green-tipped hair and proudly declares herself to be a Kamilaroi woman from up around Tamworth, the country music capital of Australia.

More here (article): https://goo.gl/x8xAaW

Karlie Noon (University of Newcastle, Australia): https://goo.gl/IaLME0

Image: https://goo.gl/S48RLq
Karlie Noon (University of Newcastle, Australia)
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Crossnumber IV
by Humbug of

Here's another chance for you to show your prowess at solving problems and possibly win £100 (local currency https://goo.gl/8bWuLG).

Rules

● Although many of the clues have multiple answers, there is only one solution to the completed crossnumber. As usual, no numbers begin with 0. Use of Python, OEIS, Wikipedia, etc. is advised for some of the clues.

● One randomly selected correct answer will win a £100 Maths Gear goody bag. Three randomly selected runners up will win a Chalkdust t-shirt. The prizes have been provided by Maths Gear, a website that sells nerdy things worldwide, with free UK shiping. Find out more at mathsgear.co.uk

● To enter, submit the sum of the across clues via this form by 7 January 2017. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 21 January 2017.

Clues and more here: https://goo.gl/ugbURe

Image: https://goo.gl/z1r2Nl
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International Survey
for and

Here's a quick survey by the Maths site about how you write fractions in the country you live(d).

I’m at the MATRIX conference in Leeds, where I’ve just been talking to Adam Atkinson. He told me that he’s trying to compile a definitive list of countries that don’t use mixed fractions.

This only makes sense if you believe in mixed fractions (and unicode character U+2062, “invisible times”)

This is going to be one of those wipe-your-bum-standing-up situations: it’s entirely possible that you can be on either side of this divide and not know the other exists. Apparently, in some countries mixed fractions just don’t exist: an integer written next to a fraction is incorrect.

So, to help Adam on his way, I thought I’d start another in our long-running series of Aperiodical Surveys. Please tell us where you live, and if mixed fractions are OK in your book.

Survey: http://goo.gl/L6qNqy
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Mini Crossnumber
by Mathew Scroggs at

For a more modest outlay of time and effort than that needed for https://goo.gl/EOstXm here is Mathew Scroggs' Mini Crossnumber!

This month I’ve put together a mini crossnumber (click here to download it). It should be possible to complete using only a pen and paper, so it would be perfect to take along to this week’s Maths Jam!

More here: http://goo.gl/C0wRj3
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Chalkdust Crossnumber 3
by

Here's another Chalkdust Prize Crossnumber set by Humbug for those of you with too much time on your hands and itchy greymatter.

You may even win a £100 Maths Gear goody bag! There is still time.

Rules

● Although many of the clues have multiple answers, there is only one solution to the completed crossnumber. As usual, no numbers begin with 0. Use of Python, OEIS, Wikipedia, etc. is advised for some of the clues.

● One randomly selected correct answer will win a £100 Maths Gear goody bag. Three randomly selected runners up will win a Chalkdust t-shirt. The prizes have been provided by Maths Gear, a website that sells nerdy things worldwide, with free UK shiping. Find out more at mathsgear.co.uk

● To enter, submit the sum of the across clues via this form by 22 July 2016. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 30 July 2016.

I think I may actually know this one...

● 39. Why is 6 afraid of 7? (3)

More clues and more here: http://goo.gl/DzVSiG

(Previous post: https://goo.gl/Y9PRbK)
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Applied Mathematical Programming

You could obtain this book at the link below for a small fee, or directly from MIT.

Do not look at the date of this book (1977). It still provides the foundation of applied mathematical programming used today. And it is still used today in modeling courses as the main reference because it covers topics from A to Z in a practical and easy-to-understand manner.

Not only does this book show you how to model a wide array of problems, it explains the mathematical algorithms/techniques behind the modeling. And it combines the theory with tonnes of examples!!!

After reading this book, I finally have a true understanding of several topics such as linear programming, duality theory, sensitivity analysis, network/dynamic programming, integer programming, non-linear programming, and my favorite, modeling/solving large-scale problems (via column generation, decomposition, etc..)

The best thing about the book is that advanced topics do not seem advanced any more!!! I wasted my \$\$\$ on too many Operational Research books that over-complicate topics; this book should be on every mathematical programmer's book shelf.

Many thanks to Bradely, Hax, and Magnanti for a job well done!

Comment by Milan Vujic

More here (US Amazon): https://goo.gl/P3Pg53

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Thinking Horizontally

Applied Mathematician u/Midtek answers the question "What would the horizon look like if you were standing on an infinitely stretching and perfectly flat plane?" using both Maths and Physics.

[...]
Ultimately, this means that the entire sky is entirely filled with images of the surface of the plane some distance away. (This is why I assumed there were no other planets, stars, etc. so that light rays do not get obstructed.) In other words, it looks as if the entire world has curved up around you and closed at the top. So it looks like you are actually in some very large spherical planet, for which the "surface" is the interior of the sphere. But remember that images above you are really emitted from points on the plane very far away. (The point directly above you is infinitely far away.) So as you walk in a straight line on the plane, you won't really see the entire sky rotating around to meet you like you would expect if you were inside a spherical planet. For instance, the point directly above you never appears to move. Try as you might, you will never reach the point where the image directly above you was emitted.
[...]

More here: https://goo.gl/Ga2MLz

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The mathematically inspired award winning architect Dame Zaha Hadid has died at the age of 65.

Born in Baghad, she studied maths at the American University of Beirut - where she later designed a building on campus which was completed in 2014 - before embarking on her career at the Architectural Association in London.

More here (article and pictures): http://goo.gl/BxVsDx

Amazingly Maths was mentioned in two of the three segments of the BBC Arts programme Front Row today.

As the death of the architect Zaha Hadid is announced, Samira talks to Sir Peter Cook, Amanda Levete and Hugh Pearman and discusses why she was such a influential, ground-breaking architect.

Jeremy Irons talks to Samira about playing Cambridge maths professor G. H. Hardy in 'The Man Who Knew Infinity' - a film based on the real life story of self-taught Indian mathematics genius Srinivasa Ramanujan.

Listen here: http://goo.gl/UtFb8R

This radio programme should be available online worldwide without restriction. It may be easiest to play on a computer (with Flash*) although it will work on iOS (with or without the iPlayer app) and once the BBC media player http://goo.gl/oHuhfM is installed, will work on Android too.

*There is now a beta for the HTML5 radio player.  It can be activated here: http://goo.gl/Ag30aB

Image: https://goo.gl/id2V0o