These dice are loaded… mathematically.
I was intrigued, so I ran the numbers myself.
Rolling 1 red you have a 17% chance of getting a 6 and an 83% chance of getting a 3.
Rolling 1 green, there’s a 50% chance of a 5 and a 50% chance of a 2
Rolling 1 blue, there’s an 83% chance of rolling a 4 and a 17% chance of rolling a 1.
To solve for the probabilities of red beating blue I added the products of the probabilities of higher numbers of red… in math terms that looks like: .17 * .83 + .83 * .17 = .28… (Probability of red being 6 * bluebeing 4 + Probability of red being 3 * blue being 1.)
I did this for all the numbers and found that Red
58% of the time, Green
58% of the time, and Blue
72% of the time.
Then I played with rolling two dice at a time, again first finding the probability of each potential outcome (this time multiplying the fraction of sides of the first number by the fraction of sides of the second number, e.g. for a red outcome of 9 I did 5/6 * 1/6 + 1/6 * 5/6), and then followed the same procedure as before to find the odds of winning with any given match up.
With two dice, Red beats Blue 52% of the time, Green beats Red 68% of the time, and Blue beats Green 68% of the time. These results are the reverse of those above.
I haven’t been blogging in forever, which I feel kind of bad about. I’m in a Master in Teaching program, though, and it turns out that grad school doesn’t leave me with an overwhelming urge to spend my spare time on the computer writing. Go figure. Anyway, I started a blog on the website I set up for students where I’ve been posting math-related stuff. I thought I’d start cross-posting it here in case any of you are interested. None of it is super high-level, since it’s for high school students, but I think a lot of it is really interesting and somewhat off-the-beaten-path. I’m just gonna post everything in this one post for now, and then from now on I’ll individually cross-post as I find things.
Remember: Only use your math powers for good
Social scientists have found that adding fake math to articles makes them more convincing. “The Nonsense Math Effect” at Washington Weekly
Math in Knitting?
Being a knitter, I had to share these sites. This isn’t the prettiest webpage, but click around and there’s a lot of really cool stuff. The Home of Mathematical Knitting shows that there is math in knitting, and that you can demonstrate really cool mathematical ideas through knitting. I love the klein, mobius and hyperbolic planes pictures. Woolly Thoughts is another math/knitting page and has a lot more pictures. I highly recommend clicking around under the Creations tab.
Math and Basketball
Math students using quadratics to model making a basket.
Google Earth, Meteors, and Math
Someone reconstructed the Chelyabinsk meteor’s path using basic geometry and algebra. (The computer skills they used were a bit more advanced, I think.) The video they used is below – they got all this information just from the shadows cast as the comet passed by. Crazy!
I think it would be unfair to talk about meteors without some awesome footage of the meteor itself. This video also shows some of the effect of the shockwave caused by the meteor. Wow!
The History of the Quadratic
has a brief history of the quadratic formula as we now know it. I never learned this in school, and I find it fascinating that quadratic relationships were first looked at about 4000 years ago by ancient Egyptian, Chinese, and Babylonian engineers trying to figure out how big to make storage spaces. The idea was developed over time all over the world, with different groups of people making different advances on the problem. I think this is one of the coolest things about math – it really is a universal language that encourages collaborative problem solving.
The BBC has a fascinating piece about the history of mathematics, this time in radio format. This 45 minute show
talks about the history of the much maligned imaginary number. Originally people just ignored square roots of negatives, even going so far as to call them “impossible” numbers. I still think imaginary numbers is a bit harsh, after all, these numbers have been shown to have very real applications in electronics, modeling fluid movement, and calculating electro-magnetic forces, to name a few.