Global Math Week and A Puzzle

It’s official! The Global Math Project team has settled on the date of October 10th, 2017, for the start of Global Math Week. From January 2017 onwards teacher and students from all across the globe will register on our website and pledge to watch and discuss our first joyous Global Math Video for the world. Not only that, we’ll release a whole suite of follow-up materials to explore and enjoy and do at home or at school that shall be forever freely available for one and all. Spread the word and take a sneak peek (https://www.theglobalmathproject.org/gmw/)!

Why 10/10/2017?

The Global Math Project is universal and we love a date that is not locked into a particular day/month/year or month/day/year format. Read the date in Australia, Bangladesh, or the U.S. and we’ll all read it the same way!

Also, we love the play with zeros and ones. Writing the date as 10|10 2017 is a subliminal nod to our first rollout topic – Exploding Dots – in particular to what we call the two/one machine.

This Month’s Puzzle

Here’s a wordless animation that illustrates the mechanics of a two/one machine. The idea presented here is the start to an incredible and astounding story that explains, in one magnificently simple fell swoop, the mathematics of place-value, school arithmetic, and advanced algebra. It’s the natural joyous way!

Can you answer the puzzle this animation leaves off with? Be sure to share with others on Facebook!

Thoughts On The Last Post

Surprise! Patterns need not be true!

dot_on_circle

Some people may get the answer 30 instead. It all depends on how you place the points around the circle. Our placement of points around the circle is unsymmetrical and so we found a central region. If you place the six points symmetrically around the circle, this middle region disappears to a point: three lines all coincide at this one point.

dot_on_circle

Using an asymmetrical placement of dots (so as to see the maximal number of pieces) one counts the following numbers of regions for different counts of dots.

dot_on_circle

Some high-school students recently studied this sequence of numbers and found – and proved – a formula for the number of pieces given the number of dots.

For n dots there are \(1+\frac{1}{2}n(n-1)+\frac{1}{24}n(n-1)(n-2)(n-3)\) pieces.

Here’s an outline of their thinking, as a series of next puzzles!

In a picture with \(n\) dots …

  • How many lines does one see?

Try drawing some pictures and writing up a table of values. Can you find – and explain – a pattern?

  • How many intersection points does one see (assuming the dots are asymmetrically placed around the circle)?

Again, count intersection points in pictures and make a table. Can you identify – and explain – a pattern?

In the picture with six dots, there are 15 lines, 15 points of intersection, and 31 pieces. In the picture with four dots there are 6 lines, 1 point of intersection, and 8 pieces.

We have \(1 + 15 + 15 = 31\) and \(1 + 6 + 1 = 8\). Coincidence?

Can you explain logically why the number of pieces one sees in a diagram must be one plus the number of lines plus the number of intersection points?

Thank you for reading, puzzling, commenting, and sharing! It means a lot to us.

More to come!

The GMP Team

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