posted by drea
Explain how you could use the Pythagorean Theorem to find the distance between the points the coordinate pair negative four comma negative three and the coordinate pair one comma one. Find the distance. You can type carat two to indicate "squared" and "sqrt" to indicate "square root." (Examples: five carat two equals five squared and sqrtsqrt twenty-five equals the square root of twenty-five)
It is easier to read and understand your prob. in mathematical form.
d^2 = X^2 + y^2,
d^2 = (x2-x1)^2 + (y2-y1)^2,
d^2 = (1-(-4))^2 + (1-(-3))^2,
d^2 = (1+4)^2 + (1+3)^2,
d^2 = 5^2 + 4^2,
d^2 = 25 + 16 = 41,
d = sqrt41 = 6.40.
Some of the steps can be omitted when you learn the operation.
, the author's not a eexrpt mathematician (in fact, he's a graphics designer who appears to be working in video games), so he may have never tried going through an explanation of Euler's formula to find out that it's not magic. I only did so myself with the help of a video lecture by Edward Burger that I found on one of his DVD courses on mathematics for The Learning Company: Burger is generally extremely clear and a good resource if you can find his stuff in your library as I did. Not sure what's available on YouTube, etc. to unpack that particular bit of mathematical magic. However, it shouldn't come as TOO much of a shock to anyone who knows at least enough about complex numbers to know that multiplying a vector by i gives a 90 counterclockwise rotation on the complex plane.All that said, the use of color in formulas seems like a great way to organize one's own thinking about what's going on as well as to do presentations to others. Might be a very nice thing to have students do for themselves/each other when they explain their ideas and problem solutions. Kids do like color and coloring, I can say that for sure based on one of the most successful units I've ever taught to alternative education students back in 1999-2000: graph coloring. Students who'd never done squat in my classes suddenly were writing A exams and enjoying themselves. Too bad I didn't figure that out a lot sooner.