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I got C’s in college math but was a little clever when I was younger. I came up with my own method for estimating square roots, which was not bad (but not nearl
by smugma 4y ago
I got C’s in college math but was a little clever when I was younger. I came up with my own method for estimating square roots, which was not bad (but not nearly as good as Heron’s method).
Find the biggest whole number less than the square root of N, call it A.
Sqrt N =~ A + (N-A^2) / ((A+1)^2-A^2)
e.g.
Sqrt 33 = 5 + 33-25 / 36-25 = 5 8/11 = 5.73
I didn’t explain it to my 5th grade teacher but told my older brother, who was taking calculus. He said I was doing a sort of Taylor expansion.
What I learned later was that I was quick at mental math and got by until I was taking real calculus, then I fell behind as I didn’t know how to learn material because of bad study habits and not being clever enough to intuitively get it (my roommate who was slightly less clever at quick math breezed through the same college math classes and became a physicist).
- madcaptenor 4y agoBasically you're linearly interpolating between, for example, sqrt(25) and sqrt(36) to get sqrt(33). That will work quite well, but it's always an underestimate.
- smugma 4y agoThat’s a concise summary, thank you!