To begin the carnival we will as is the tradition look at some properties of the number 22, additionally we can look at some sites which provide information on number properties.

A good place to start is the **NumberADay blog **from the** Mathematical Association of America**. Every working day, they post a number and offer a selection of that number’s properties.

**Here** we learn for example that 22 is a pentagonal number and is the smallest number that can be expressed as the sum of two primes in three ways: **22 **= 3 + 19 = 5 + 17 = 11 + 11.

A great site for finding out about the properties of a number is Tanya Khovanova’s Number Gossip. Whilst we all know that 22 is even, did you know it is odious?

From **Cool Numbers **we learn that 22 is seriously cool!

For other sites with information on number properties see **What’s Special About This Number?**, **Amazing Number Facts, **a site with many fascinating articles and **Mudd Math Fun Facts**, where we could search for all the **Number Theory Fun Facts**. We could of course enter **22 as a WolframAlpha query**.

So, to the posts, as it’s a carnival it seems appropriate to start with the party post!

**Birthday Party Fibonacci Style!**

Bon Crowder describes a fabulous party for her soon to be three year old in **Birthday Party Fibonacci Style!** There are some fabulous ideas here, I want a party like that!

### Asymptotes

Shaun Klassen presents a clear description with accompanying diagrams in his **Asymptotes** at **Maths Concepts Explained**. Reading Shaun’s post it struck me that we could provide a Desmos graph where students could experiment (click on the image and change the sliders).

For more on the outstanding Desmos graphing calculator see **my own series of posts**.

### Summer Maths Series

One of Rocky Roer’s series of Summer Maths series posts is **What’s the comma good for? **where he describes what you can do with that comma key on your calculator!

In case anyone is wondering about the calculator font I have been using, you can download such fonts free. The Calchux font is available on the **resources page** (scroll right down to Miscellaneous) of **subtangent.com.**

**Making a singular matrix non singular**

John Cook was asked this question on Twitter ‘Is there a trick to make an singular (non-invertible) matrix invertible? He posted his response **Making a singular matrix non singular** on his blog **The Endeavour**. John’s mention of Twitter reminded me of the **value of developing contacts on Twitter**.

### The Man Who Solved a Math Problem for 8 Years

Guillermo Bautista tells the story of Andrew Wiles in solving Fermat’s Last Theorem in his post **The Man Who Solved a Math Problem for 8 Years** on Math Palette.

### 10 Reasons Why Mathematics Teachers Should Blog

It seems most appropriate to conclude the carnival with Guillermo’s post on **10 reasons why Maths teachers should blog**. I know I have learned a great deal, found a fantastic library of resources and made many contacts since starting my own blogs. Thank you so much to all of the contributors here.

That concludes this edition. Thank you for reading. Submit your blog article to the next edition of** **Mathematics and Multimedia Blog Carnival#23 (a happy event as 23 is a **happy number**!) which will be published on **Math Palette** using our **carnival submission form, **the deadline for submitting articles is August 18th.