I usually hate stream-of-consciousness writing. It confuses and irritates me. (See "Susie Asado," by Gertrude Stein.) However, the poem "Jam," by Karen Chase, is a definite exception. The stream-of-consciousness style fits the subject matter of "Jam" perfectly. The end result is unique, interesting, and very enjoyable. You can read "Jam" here.
Wednesday, April 23, 2008
Saturday, April 12, 2008
π
I wrote a calculator program a couple days ago to calculate pi. It was a very interesting experiment!
I used a Taylor series to do this. If you let f(x) = arctan(x), then if x = 1, f(x) = π/4. So if you calculate the Taylor series for f(x), the sum as the number of terms approaches infinity will approach π/4. Here's the series:
∞
y = Σ (-1)^(n-1) * x^(2n-1) / (2n-1)
n=1
Let x=1, and then multiply the series by 4.
I programmed my brother's TI-84 Plus SE (because that's much faster than my TI-83) to calculate about 10,000 terms of the series. The calculator thought for about two minutes, and returned an answer that was only correct to four or five digits. That gave me a new respect for supercomputers that can calculate billions of digits of pi! I wish I knew of a way to plug this equation into our computer and see how it did.
I used a Taylor series to do this. If you let f(x) = arctan(x), then if x = 1, f(x) = π/4. So if you calculate the Taylor series for f(x), the sum as the number of terms approaches infinity will approach π/4. Here's the series:
∞
y = Σ (-1)^(n-1) * x^(2n-1) / (2n-1)
n=1
Let x=1, and then multiply the series by 4.
I programmed my brother's TI-84 Plus SE (because that's much faster than my TI-83) to calculate about 10,000 terms of the series. The calculator thought for about two minutes, and returned an answer that was only correct to four or five digits. That gave me a new respect for supercomputers that can calculate billions of digits of pi! I wish I knew of a way to plug this equation into our computer and see how it did.
Poetry
I've been taking a course in and extracurricularly studying a lot of poetry lately, as part of my preparation for the English Literature AP exam which I so stupidly signed up for. I didn't know very much about poetry before, so I've been finding this very interesting.
- Poetry is approachable, and by normal people. It can be read, understand, and enjoyed.
- Poetry is very interesting. Poets express extremely complex thoughts in the most compact, effective way possible.
- Poetry appeals intellectually. For me, poetry requires more brainpower than prose. You have to really concentrate to read and interpret poetry, because poets don't waste words. Even the aesthetic aspects of poetry are intellectually interesting (e.g. seeing how the poet's use of devices such as alliteration, assonance, meter, etc. make you feel a certain way).
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