Erik's Blog

The other day I was looking at a framed photo in my house and wondering how the area of the border around the picture (called a mat board in the framing industry) compared to the area of the picture itself. Immediately I remembered the master of all aesthetic ratios, the golden ratio, Phi! 1.61803398874989… I thought, “I bet if the ratio of the area of the picture to the border was Phi, it would look good!” So I set off on an algebraic quest to find the answer…
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Any intelligent person knows that Sarah Palin was joking when she said that she could see Russia from her house. It’s pure hyperbole. But everyone in the media keeps repeating it over and over, and I’m certain that some people probably actually believe it to be true. I bet that even the people that understand the hyperbole probably don’t realize just how much of an exaggeration it really is. So I decided to use my Distance To Horizon Calculator to see just how tall Governor Palin’s house would have to be in order to see the Russian coast.
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The flowers of Passiflora edulis are gorgeous. I particularly like the Fibonacci numbers of stamens, three of one kind, and five of another. Fibonacci numbers are, of course, related to the Golden Ratio, which is pretty much the mathematical definition of beauty.

At this time of year, these passion flowers are blooming vigorously here. Later, they will turn into passion fruit. (more…)

It might not be possible to have too much fun, but it’s definitely possible to have to much Phun. Phun is a "2D physics sandbox". What that means is that it allows you to draw shapes (circles, squares, or arbitrary freehand shapes) and then lets you bang them together using simulated physics laws. Check out the video at the link above for a demonstration.

Phun is exactly the kind of computer "game" that my brain adores. I used to play hours and hours of The Incredible Machine, which is a very similar concept. For me, at least, Phun is seriously addictive. It’s like crack for Newtonian physics lovers.
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A couple years ago, a friend and I, while staying at a beachside condo, were standing on the balcony staring at the flat, distant horizon, and we got to wondering, "I wonder how far we can see right now?" and "I wonder how much further we can see up here on the 9th floor than the people out there on the beach?" Unable to resist, I got out a pen and paper and started drawing circles and right triangles, and we quickly had our answer. I was pleased that I still had the trigonometry knowledge to figure out the answer to such a question.

So hold on tight, because here we go, on a trigonometric journey to the end of the Earth! (more…)