Plus Blog

December 11, 2015

It's Friday. Time to decorate your office with your office stationery!! Turn your humble post-it notes into a beautiful skeletal dodecahedron. We can personally confirm that it is ridiculously satisfying making these and your desk will be the envy of your workplace. They even make great decorations for the Christmas tree!

Find out how to make one on the Wild maths website!

Wild Maths encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

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December 10, 2015
Average

There are several different notions of average: the mean, the median, the mode and the range (see below for the definitions). If you work out each of these for the set of numbers 2, 5, 5, 6, 7, you'll notice something interesting — they are all equal to 5!

Can you find other sets of five positive whole numbers where mean = median = mode = range?

How many sets of five positive whole numbers are there with mean = median = mode = range = 100?

This puzzle comes from our sister site Wild maths, which encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. Visit Wild maths for more games, investigations, stories and spaces to explore!

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Definitions

Given a list of $n$ numbers $x_1,$ $x_2,$ $x_3,$ up to $x_ n,$ (ordered by size) the mean is

  \[ \frac{x_1+ x_2 + ... x_ n}{n}. \]    

The median separates the lower half of the list from the higher half. It is the middle number if there are an odd number of numbers in the list, or the number half-way between the two middle numbers if there are an even number. So, assuming that $x_1 \leq x_2 \leq x_3 ... \leq x_ n.$ The median is

  \[ x_{(n+1)/2} \]    

if $n$ is odd and

  \[ \frac{x_{n/2} + x_{n/2+1}}{2} \]    

if $n$ is even.

The mode is the number in the list that occurs most often — which means that there can be more than one mode.

The range is the difference between the largest and the smallest number in the list:

  \[ x_ n - x_1. \]    
December 9, 2015
Rachel, Manjul and Marianne

Manjul Bhargava (centre) with Plus editors Rachel and Marianne

Manjul Bhargava's idea of mathematics is interesting: "I think that the reasons for doing maths are similar to those for doing music or art," he says. "It's about contributing to a certain understanding of the world and ourselves." Bhargava has been described as having "extraordinary creativity" and was awarded the Fields Medal in 2014, one of the most important prizes in mathematics.

Bhargava believes that one of the keys to solving hard mathematical problems is to look at them in a new way: he famously solved an old number theory problem by visualising it as a Rubik's cube. You can meet him and his work on Wild Maths, and find out more detail in the Plus articles Revealing numbers and Answers on a donut, and listen to our interview with him from 2014.

Wild Maths encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

Return to the Plus Advent Calendar

December 8, 2015

We've read the book. We've bought the T-shirt. And now, finally, here it is: the movie of one of our favourite maths problems, the bridges of Königsberg. Though admittedly, we made it ourselves. We learnt several interesting lessons in the process. For example that a bin doesn't make a good supporting character and that people who shouldn't be in the frame should get out of it. But other than that, we're well on course for an Oscar! And we believe that the solution to this problem is a true example of mathematical creativity.


You can read more about the bridges of Königsberg here.

This video was inspired by content on our sister site Wild Maths, which encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

Return to the Plus Advent Calendar

December 7, 2015
Gallery

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Can you cut up an old playing card to make a hole big enough to walk through?

Have a go! If you struggle, visit Wild Maths, where you can get some ideas and also find other things to do with paper and scissors.

Enjoy!

Wild Maths encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

Return to the Plus Advent Calendar

December 7, 2015

Sometimes a piece of mathematics can be so neat and elegant, it makes you want to shout "eureka!" even if you haven't produced it yourself. One of our favourite examples of this is the art gallery problem.

Gallery

The Guggenheim Museum in Bilbao: hard to supervise. Image: MykReeve.

Suppose you have an art gallery containing priceless paintings and sculptures. You would like it to be supervised by security guards, and you want to employ enough of them so that at any one time the guards can between them oversee the whole gallery. How many guards will you need?

Think about this for a while (go on, it's Sunday) and once you've had enough, read about the answer and its proof here. It's pure genius!

This article was inspired by Wild Maths, which encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

Return to the Plus Advent Calendar

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