The Bases are Loaded

The base of any number system is the number of different symbols used to compose the numbers. The system we use, base 10, is such because there are ten symbols used to form the numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. It is assumed that we use this system since we have 10 digits on our hands. People found it easier to count using base 10.

The cool thing about numbers is that we can play in other bases. The binary system, base two, has only two digits: 0, 1. Computers perform their calculations in binary codes.

Here is your challenge for today: Using the examples below of Base Ten, Base Two, and Base Five, write the numbers from one to twenty in base 8. Ready, go!

BTW: The answer to the last challenge is in the comment section of that post.

Base Ten	Base Two	Base Five	Base Eight
1	1	1	1
2	10	2
3	11	3
4	100	4
5	101	10
6	110	11
7	111	12
8	1000	13
9	1001	14
10	1010	20
11	1011	21
12	1100	22
13	1101	23
14	1110	24
15	1111	30
16	10000	31
17	10001	32
18	10010	33
19	10011	34
20	10100	40

Types of Prime Numbers

Time for a little math. I have been writing about lots of things and realized that math was deficient. How about a little fun with prime numbers?

Quick review: Prime numbers are natural numbers that have only two factors: 1 and the number.

Some special types of prime numbers (you didn't think that mathematicians would stop at one definition, did you?):

• Twin Primes - a set of two consecutive odd primes, which differ by 2. Examples: 3 and 5, 5 and 7, 11 and 13.
• Symmetric Primes, also called Euler Primes - a pair of prime numbers that are the same distance from a given number on the number line. Examples: Given 6, 5 and 7 are symmetric primes. Given 16, 3 and 29 are symmetric primes.
• Emirp - a prime number that remains prime when its digits are reversed. (Emirp, of course, if prime spelled backward!) Examples: 13 (31), 347 (743).
• Relatively Prime Numbers - numbers whose greatest common factor is prime. These numbers are not necessarily prime. This definition is referring to the relationship between numbers rather than the numbers themselves. Examples: 4 and 9, 10 and 27, 8 and 9.

So now, the questions to ponder/work on:

1. Can you find all of the symmetric primes for 24? (hint: there are more than 3 pairs - and no, I am not telling how many there are. That would spoil the fun!)
2. How many emirps exist between 1 and 200? (The number when it is listed its initial way - so 13 and 31 would each count as unique emirps.)

Ready..... Go!

Math and Religion?

I enjoy listening to a radio program called "Speaking of Faith". I like the overall feel of the program. There are discussions about a variety of topics and it is a "judgement free zone". (My words, not theirs) I have learned a little about other faiths and some of the things people are doing in the pursuit of meaning in the modern world. I did not expect something to stimulate my math brain at the same time.

Last Sunday, as I was contemplating getting ready for church, the program came on. I always listen a little to see if the content will be worth the consequences of having to rush to get ready. (It usually is.) I chose to listen to the program in it's entirety. I was intrigued by the content and the discussion.

The show was called, Who Ordered This? New Mysteries of an Expanding Universe.
Astrophysicist Mario Livio works with the Hubble Telescope's findings on phenomena like dark energy and white dwarfs. We explore edges of discovery where scientific advance meets recurrent mystery — questions richer than any of their current answers.

I invite you to visit the Speaking of Faith website and listen in or download the podcast if you like things like fibbonacci numbers, the golden ratio and marveling about the mathematical beauty of our world. The link takes you directly to the story.

http://speakingoffaith.publicradio.org/programs/2010/who-ordered-this/

This is the link for the discussion blog as well. This is what originally caught my eye. I enjoy thinking about mathematics in nature. Interesting ideas!
http://blog.speakingoffaith.org/post/617552387/mathematics-in-sunflowers-shubha-bala-associate

Fun Night with Steven Strogatz

Monday night, I had the opportunity to meet Steven Strogatz. He is a mathematician, author and a professor at Cornell University. I have posted some of his writings here on my blog in the past. Currently, the work that I am a fan of are his articles written for the New York Times website. I will post the link again because if you haven't seen these, I think you will enjoy then when you do.

Imagine how excited I was when I found out that Math for America was hosting an hour-long lecture where Mr. Strogatz would talk about his series of online articles! Of course I was thrilled, so I dressed up and went. The lecture lasted an hour, but it felt like 20 minutes. He started by talking about the meeting with the NY Times editor who asked him to write the series. He discussed the process by which he decided his topics, audience and voice of the articles. The session was interactive, too. We were all given the opportunity to share what we would have done if we were in his place.

Hearing about his creative process and having another chance to see some of the content was entertaining and educational. The playful tone you read in the articles is true to the man when you meet him in person.

If you haven't, read some of the articles. You won't be sorry, and you might learn something or see something in a way that makes you think. I have included the link to the most recent article. It's time to kindle or rekindle your love of math!

Steven Strogatz in the NY Times.