Taylor’s polynomials and Maclaurin series in action

Illustration of Taylor's series

From the top to the bottom, as my eyes moves along the gradual descend, I see a series of numbers. Perhaps, Taylor’s polynomials could describe these better.

Aerial photographs brought it to perspective. Those taken from the front, side, rare or above it, they all depict one thing. The convergence or divergence of series of numbers. Truly, the teacher was right. Mathematics is real. I see a series of numbers.

Up in the planes, it is just a pattern of concentric squares with common center, all vanishing at the center. Oh, I it is true, the series is converging to a point. The point is zero. When I think keenly about it, I see a series of numbers

I had not known what Taylor’s polynomials are. I have neither heard of power series. It is the most abstract one, convergence of series that my sister sings every day. A chorus that their teacher taught them so that they may always remember it. I did not know it could be visualized. Really, I see series of numbers.

I had not known that mathematics could be that beautiful. Marrying tourism and landscaping, or rather, exterior designs. My eyes cannot allow me to move away from it. They, just, want me to see the series of numbers.

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Even architects can think along these lines! Bring series, sequences, and convergence into perspective! I am sure that my sister will now understand what Maclaurin series is together with their special case, the mean value theorem and connect all these with Taylor’s polynomials. Moreover, proudly explain it to the fellow students because mathematics is now real, courtesy of seeing the series of numbers.

Yes! I have now realized, as I see the series of numbers, that everybody played his/her part. The architect got it right from the calculus class. The architect’s teacher provided the right materials. The artisans did theirs too: and me? I am challenged. I am must be counted too. As I pass by here every day to admire this building: while, at the back of mind, appreciate Taylor’s work in action, I must get the right person to drive the concept home. This must be the best AP calculus tutor or a calculus tutor. Off course, the cheapest tutor to make me see the series of numbers elsewhere too.

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Jack SI

This is a really very interesting blog post.
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