# IntMath Newsletter: Interactive 3D graph, Polymath

By Murray Bourne, 19 Apr 2016

19 Apr 2016

In this Newsletter:

1. New 3D interactive graph

2. Over 70 interactives

3. Roller door problem and Polymath software

4. Math in the news

5. Math puzzles

6. Math movie: Math symbols in ancient rock art?

7. Final thought: Mathematical habits of mind

## 1. New 3D interactive graph

## 2. Now over 70 interactives!

There are now over 70 interactive math applets (most of them mobile-friendly) on IntMath. I recently updated the full list, which you can find here: |

## 3. Roller door problem and Polymath software

Here's a numerical solution to an earlier problem we discussed involving the height of a roller door given the number of turns the door makes. |

## 4. Math in the News

### (a) Andrew Wiles receives Abel Award for solving Fermat's Last Theorem

Sir Andrew Wiles solved Fermat's Last Theorem in 1994. He proved there are no integer solutions for y = ^{n}z. ^{n}Wiles was recently awarded the Abel Prize "for his stunning proof of Fermat’s Last Theorem by way of the modularity conjecture for semistable elliptic curves, opening a new era in number theory". |

His prize money is equivalent to $850,000 (USD).

Last year's joint winners for the Abel Prize were John F. Nash Jr. (who was the subject of the movie *A Beautiful Mind*) & Louis Nirenberg.

### (b) Math Awareness Month: Making Predictions

April is Math Awareness Month, and the theme this year is "Making Predictions". It's a good theme, and one that we should encourage more in mathematics courses. Making predictions requires |

The articles on the past, present and future of prediction and the central position of mathematics and statistics are quite interesting.

## 5. Math puzzles

The puzzle in the last IntMath Newsletter asked about a journey by two girls involving a bicycle and/or walking.

Correct answers with sufficient explanation were given by: Chris and Hamid. There was certainly an interesting assortment of solutions for this one!

### New math puzzle

The Egyptians used **unit fractions**, where the numerator was always 1.

They would need to write their ratios as the sum (not difference) of unique unit fractions, like this:

Using this system, how would they have written ?

You can leave your responses here.

## 6. Math movie: Geometric shapes in ancient rock art paintings

Ancient rock art may give clues to the origin of written symbols, including early math notation. |

## 7. Final thought: Mathematical habits of mind

In the article Mathematical Habits of Mind, Cindy Bryant discusses the importance of developing sound strategies for solving math problems. Expert problem solvers don't panic when they come across an unfamiliar problem. They will use one or more of the following strategies (based on Polya''s four-step problem solving process) until something "clicks":

Draw a picture

Find a pattern

Make a list

Make a table

Solve a simpler problem

Guess and check

Act out the problem

Work backwards

Write an equation

Until next time, enjoy whatever you learn.

Image credits for this Newsletter:

See the 15 Comments below.

19 Apr 2016 at 11:15 am [Comment permalink]

Subtract 1/2 from 11/13.

From that subtract 1/3.

This last difference is 1/78.

(1/2)+(1/3)+(1/78)= 11/13

No wonder only priests and builders used fractions.

-----------------

Well done 3D applet.

Far better illusion than my hand drawings.

You may eventually offer an option

to viewers with VR googles.

ct

19 Apr 2016 at 6:18 pm [Comment permalink]

Good problem!

11/13 = 1/2 + 1/3 + 1/78

20 Apr 2016 at 1:27 am [Comment permalink]

We know that

And that

So we conclude that

And finally

Using the same technique for

And

Then

We still need to clear the duplicates

And the answer would be

20 Apr 2016 at 2:42 am [Comment permalink]

1/2 + 1/3 = .833333 close to 11/13

let x= 11/13 - .833333, and y =1/x

By searching, y=78. So 1/2 +1/3 + 1/78 = 11/13

20 Apr 2016 at 10:08 am [Comment permalink]

1/2 + 1/3 + 1/78 = 11/13

20 Apr 2016 at 3:07 pm [Comment permalink]

It is more than ,this minus and get the answer:

20 Apr 2016 at 3:09 pm [Comment permalink]

Hi Murray

Hope you are well. I am still so thankful to you for your help with maths on internet 🙂

Regards

Rika

20 Apr 2016 at 7:08 pm [Comment permalink]

I'm well, Rika, and you're welcome!

21 Apr 2016 at 7:58 pm [Comment permalink]

The unit fractions, in decreasing order of size, are 1/2, 1/3, 1/4, 1/5 and so on.

11/13, the fraction that we need to convert to unit fractions, Egyption-style, is nearly one. Definitely bigger than 1/2, so let's subtract 1/2 and see what we're left with:

11/13 - 1/2 = 22/26 - 13/26 = 9/26.

So we know that 11/13 = 1/2 + 9/26. We're making progress, but there's still more work to do.

9/26 is just a tiny bit bigger than 1/3, so let's take that away and see what remains:

9/26 - 1/3 = 27/78 - 26/78 = 1/78. Which, happily enough, is also a unit fraction.

Putting it all together, we can see that:

11/13 = 1/2 + 1/3 + 1/78. Numbers that the Eqyptians can relate to.

21 Apr 2016 at 9:01 pm [Comment permalink]

So thank you for this wonderful effort

11/13 = 1/2 + 1/4 + 1/13 + 1 /52

24 Apr 2016 at 2:40 am [Comment permalink]

11/13 = 1/2 + 1/4 + 1/13 + 1/52

27 Apr 2016 at 11:00 am [Comment permalink]

1/2 + 1/3 + 1/26 = 11/13

5 May 2016 at 5:35 am [Comment permalink]

11/13

= 22/26

= 13/26 + 9/26

= 1/2 + 18/52

= 1/2 + 13/52 +5/52

= 1/2 +1/4 + 4/52 +1/52

= 1/2 + 1/4 + 1/13 + 1/52

=

............

I I + IIII + n + III + n+n+n+n+n + II

Graphic limited ! Bah

5 May 2016 at 5:52 am [Comment permalink]

My graphic looked OK in preview comment,

but lost numerator symbols when submitted.

So for clarity I've separated my 4 fractions, omitting the numerator symbol.

II, IIII, n+III, n+n+n+n+n+II

Furthermore the +'s may be omitted, if the numerator symbols are assumed to be added.

Yielding,

II, IIII, nIII, nnnnnII

24 May 2016 at 11:30 pm [Comment permalink]

I split it into 3, and I got:

1/3 + 1/2 + 1/78

I times it through by 3, so I could split it into 1 third and then got a half from that and realised the remainder was only one.