Tag: number theory

19 February 2015

February 19th, 2015

Dear Theory Makers,

The world bombards our human senses with stimulation–birds chirping, sun rising, shadows stretching, stars a-twinkling. Luckily, we humans are pretty good at finding patterns in these experiences. If we’re smart, we track these patterns, combine them with our human reason, and turn them into theories about how the natural world works.

This reminds me of an argument I often have with myself: can humans know all of nature’s secrets? Sometimes, when I think of how much humans already know about the universe (especially the ideas about how it began billions of years ago) I think we can. Other times, I think nature’s just too complex for the feeble human mind to really understand.

But there’s one thing I know for sure: It’s always worth trying.

Sincerely,

Mr. H
September 7, 2012

September 6th, 2012

Dear Searchers and Seekers,

Today’s probably my favorite lesson of the year. We’re going to find all the prime numbers through 100 by using the sieve of Eratosthenes. Eratosthenes was a Greek scientist and mathematician from over 2000 years ago, but he knew things that people would have to relearn. He not only knew the earth was round, but he was able to measure its circumference within 2%. He also drew a map of the world, was a poet, a musician, and an athlete. He’s one of my personal heroes.

Eratosthenes’s sieve shows us the power of faithfully following a simple and clever method. Today, we have supercomputers that find insanely large prime numbers, but the work of creating a method and following it will never be replaced by computers.

Remember, math is the science of patterns. As we’re messing around with multiples, be on the lookout for the beautiful and intricate patterns that dance all through our amazing number system.

To the hunt (for primes),

Mr. Heimbuck
September 5, 2012

September 4th, 2012

Dear Number Classifiers,

Humans make sense of the world by classifying it. We put like things in one heap and different things in another. We do the same thing with numbers. There are endless ways to classify numbers, but mathematicians have agreed on a few ways that are most useful. You’ve already learned how to classify numbers as odd and even. Yesterday we talked about classifying numbers by their divisibility. Today we’re going to talk about classifying numbers as prime or composite (or neither!).

Prime numbers are an interesting topic, and they’re important to our everyday lives. We won’t quite get into cryptography today, but you have prime numbers to thank for keeping your secrets secure in the digital world. Mostly, we’ll think and talk about the strange but illuminating nature of prime numbers. Their charm might just convince you that there’s some kind of logic lurking behind the universe’s deepest mysteries.

Happy Classifying,

Mr. Heimbuck

Tag: number theory

19 February 2015

September 7, 2012

September 5, 2012