Scientist have begun to realize that they can tackle big problems by harnessing the power of the internet to enlist “citizen scientists” to “crowdsource” their projects. The search for large prime numbers is one such project. Citizen mathematicians can become part of the search for prime numbers by joining the Great Internet Mersenne Prime Search (GIMPS). Mersenne primes (prime numbers of the form 2n-1) are extremely rare (only 48 are known).
All you need to participate is a computer, an internet connection, and patience. Simply download the GIMPS software from their website and start it running. The program runs in the background in the lowest priority, so it shouldn’t affect your computer performance. The patience is needed because you may need to run the program for weeks to complete a primality test. I downloaded the program last week and have been running it ever since, and I’m only up to 3%. It helps if you have a computer that is running most of the day. You can learn more about the math involved in the primality testing on the GIMPS math page.
And, if just knowing that you are helping advance the field of mathematics isn’t enough to entice you, there is also a $3,000 cash award to participants finding a prime having fewer than 100,000,000 digits and a $50,000 award to the first participant to find a prime with greater than 100,000,000 digits.
Mersenne primes are named for Marin Mersenne (1588– 1648), French theologian, philosopher, mathematician and music theorist.
You may know that Alice’s Adventures in Wonderland was written by Lewis Carroll, but did you know that his real name was Charles Dodgson and that he was also a mathematician? Many mathematical concepts can be found in Alice’s Adventures in Wonderland if you look for them, and some have suggested the novel was written as a satire on the new modern mathematics emerging in the mid-19th century.
Read more in these articles at:
io9 – A Math-Free Guide to the Math of Alice in Wonderland
New Scientist – Alice’s adventures in algebra: Wonderland solved
Sometimes it can be useful to be able to quickly determine is divisible (meaning it can be divided evenly) by a certain number. Whether you are trying to evenly divide a set of objects among a group of people or simplifying a fraction, knowing these divisibility rules can be a big help.
You can download a B&W pdf version here.
My previous post about platonic solids included a link to a site with printable templates for making your own solids. However, there are other easy ways to make paper platonic solids. Here are directions for making a tetrahedron using an envelope.
Step 1. Seal the envelope and then fold length-wise to mark the center line. I have marked the center line with a dotted line. (Marking the line is optional, I was just trying to make it more visible.)
Step 2. Fold the top corner down to the center line. The fold should extend down to the bottom corner.
Step 3. Fold opposite side over until it touches the corner that was folded down. This is to find the line perpendicular to the center line that touches point where the corner touches. I’ve marked this with another dotted line.
Step 4. Cut along the vertical line and unfold the corner.
Step 5. Fold the two corners on the open end of the envelope from the center line to the opposite top corner. These folds are marked with the highlighted lines. Fold forward and back to make a good crease.
Step 6. Open up envelope at the cut end and pop out the 4 folds you made (the highlighted folds plus the corresponding ones on the opposite side). Tape the open end together and you have your completed tetrahedron.
Very big and very small numbers can be hard to comprehend. Having visualizations and videos, like the one below, can helpful in understanding what all those zeros mean. (Although, it can still be hard to wrap your mind around the scales involved.) This videos zooms out to 1024 meters and then back in to 10-16 meters. This range is smaller than that of of the Scale of the Universe site (1027-10-35 meters) mentioned in my previous post about the very big and the very small, but it was made over 35 years ago.