# IntMath Newsletter: Open source textbooks, math of beauty

By Murray Bourne, 14 Jan 2014

14 Jan 2013

In this Newsletter:

- Resource: Open source textbooks
- Updated math interactive - Math of beauty
- IntMath Polls
- Math puzzle
- Friday math movie - Sand images drawing machines
- Final thought - School for the soul

## 0. Greetings

Happy New Year, everyone! I hope 2014 is kind to you, and that you learn a lot.

I usually don't blog much during the end of year period, mostly because people are not very interested in math then! (How do I know? See Thanksgiving for less math where I show what happens to IntMath traffic each festive season.)

IntMath recently passed some milestones:

- There are now over 13,000 people subscribed to the IntMath Newsletter. Welcome to all of you, especially the newcomers!
- There are over 4,000 people following IntMath on Twitter. I used to think Twitter was a useless time sink, but now that I'm part of an educational community that shares lots of interesting and useful things, I've changed my mind.

I love hearing from readers and was delighted to receive this from Rachel in Ireland:

"Dear Murray

I have never met you in person, but you need to know how much help your IntMath Newsletters were to me whilst I was studying. I returned to college as a mature student so needed every bit of assistance I could get, and found that through your newsletter and site. Thank you so much."

You're very welcome, Rachel!

On with the Newsletter.

## 1. Resource: Open source textbooks

Unfortunately, this resource has since disappeared.

## 2. Updated math interactive - Math of beauty

This page has always been one of the most popular on IntMath. I updated it so it also works on tablets and (large?) smart phones.

This interactive allows you to place a mask over the photos of "beautiful" people, and see how close their face is to the "ideal". See: Math of Beauty (you'll find the mask interactive about 1/2 way down the page) |

**Skin deep? **On the page, I have a disclaimer that says "inner beauty is more important than external beauty.". As I said, this is not a serious piece of science!

## 3. IntMath Polls

Studies show one of the biggest impacts on student learning is the quality of the teaching. This poll is consistent with that finding.

The poll during Nov/Dec 2013 asked readers:

**What would have the biggest positive impact on your enjoyment of school?**

Better teachers: 44%

Learn more about real life issues: 34%

Reduce bullying: 11%

More technology: 11%

Total votes: **1200**

**Current IntMath Poll: **Considering the above result, the current IntMath Poll asks what teachers should do to improve learning outcomes. You can answer on any (inner) page of IntMath.com.

## 4. Math puzzles

The puzzle in the last IntMath Newsletter asked about the least 2 positive integers with certain remainders.

The question I asked is actually very old. It was posed by the Chinese military general, strategist and philosopher Sun Tzu in the 1st century CE. (Yes, the guy who wrote *Art of War*.)

Correct answers with explanation were given by Nicos and Hamid.

**New math puzzle**

A 2000-page book has pages numbered consecutively from 1. What percentage of the pages contain a 5 in the page number?

Leave your responses here.

## 5. Friday math movie: Four Cable Drawing Machine

This reminds me of Spirograph images that brought art and geometry together, and always had an element of mystery to them. Watch: Four Cable Drawing Machine |

## 6. Final thought: School for the soul

"Think of life as a school for your soul; you are here to learn in perfect well being. Here's a tip for life's pop quizzes: instead of asking why something happened, ask instead 'what can I learn?' For extra credit, ask '...and how may I serve?'" [Jackson Kiddard]

Until next time, enjoy whatever you learn.

See the 8 Comments below.

15 Jan 2014 at 1:38 am [Comment permalink]

Answer: 542.

In a given set of numbers from 1-99, we have 19 (two-digit) numbers containing 5, namely 5, 15, 25, 35, 45, 50-59, 65, 75, 85, and 95.

Therefore, the pages numbering xy05, xy15, etc. will include a 5, where x can be 0 (for pages 1-999), 1 (for pages 1000-1999), or 2 (for page 2000), and y can be 0-9. (I am treating the 2000 pages as four-digit numbers; 0010-0099 would be pages 10-99 and 0100-0999 would be pages 100-999.)

Then pages 1-499 would have five groups of 19 pages which contain a 5.

Pages 500-599, of course, have all 100 pages containing a 5.

Pages 600-1499 have nine groups of 19 pages.

Pages 1500-1599 have 100 pages.

Pages 1600-2000 have four groups of 19 pages.

The total is (19 x 5) + 100 + (19 x 9) + 100 + (19 x 4) = 542.

15 Jan 2014 at 2:20 am [Comment permalink]

27.1%

for every 10 pages, there's 1

for every 100 pages, there's 10 for the 50s and 9 for the other 10s -> 19

for every 1000 pages, there's 100 for the 500s, and then 19 for each 100 -> 100 + 9*19

for 2000, it's 2*(100+9*19) -> 542 -> 27.1%

16 Jan 2014 at 1:38 am [Comment permalink]

Hi, Dear Murray.

Thank you for all yours efforts to keep us up to date in maths.

I want to wish you (late) a Great New Year and letÂ´s go ahead.

Kind regards

Bruno

16 Jan 2014 at 8:05 am [Comment permalink]

You're welcome, Bruno!

16 Jan 2014 at 8:14 am [Comment permalink]

200

17 Jan 2014 at 2:44 am [Comment permalink]

If the definition "...a 5..." means "pages which contain at least one 5" (and not "only one 5"), then, the series 1 to 10 contains one 5. The series 1 to 100 contains 9*1 plus 10 (the ten from 50 to 59)= 19 pages with 5s. The series 1 to 1000 contains 9*19 plus 100 (the hundred from 500 to 599)= 271 pages with fives. So, there are 542 pages that contain at least one five in the 2000 pages book. That means a percentage of 27.1%.

17 Jan 2014 at 3:55 pm [Comment permalink]

Dear sir,

We can solve this using sets concept. The goal is first finding the

number of page numbers containing a (i.e. only one) 5.

Let

A=page numbers containing first digit as 5

B=page numbers containing second digit as 5

C=Page numbers containing third digit as 5

number of page numbers containing only one

5=n(A-(BUC))+n(B-(AUC))+n(C-(AUB))=81+81+81=243 in 1000 pages.In 2000

pages 2X243=486 page numbers contain only one 5.

percentage is 486X100/2000=24.3%

If the problem asks about how many pages contains atleast one 5, then

it can be solved using addition law of sets which gives answer 27.1%

25 Jan 2014 at 3:16 pm [Comment permalink]

number of pages have only one 5 :

1-digit :1

2-digit :17

3-digit :225

4-digit :486

percentage=36.45%