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Calculus in Bathroom Tiling

Calculus concepts like optimization and the fundamental theorem of calculus can be useful when retiling areas with irregular shapes that do not conform to standard geometric formulas. When trying to fit tiles around asymmetric objects like toilets or sinks, calculus allows you to calculate the precise area to determine how much of each tile needs to be cut or added. This is an example of using Riemann sums, which break a curve into rectangles to measure its area, and are an important conceptual introduction to the fundamental theorem of calculus.

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81 views2 pages

Calculus in Bathroom Tiling

Calculus concepts like optimization and the fundamental theorem of calculus can be useful when retiling areas with irregular shapes that do not conform to standard geometric formulas. When trying to fit tiles around asymmetric objects like toilets or sinks, calculus allows you to calculate the precise area to determine how much of each tile needs to be cut or added. This is an example of using Riemann sums, which break a curve into rectangles to measure its area, and are an important conceptual introduction to the fundamental theorem of calculus.

Uploaded by

suprabhatt
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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RE-TILING THE BATHROOM // CALCULUS

ISTOCK

Many students don't get to calculus in high school, or even in


college, but a cornerstone of that branch of math is optimization —or
figuring out how to get the most precise use of a space or chunk of
time.

Consider a home improvement project where you're confronted with


tiling around something whose shape doesn't fit a geometric formula
like a circle or rectangle, such as the asymmetric base of a toilet or
freestanding sink. This is where the fundamental theorem of
calculus—which can be used to calculate the precise area of an
irregular object—comes in handy. When thinking about how those
tiles will best fit around the curve of that sink or toilet, and how
much of each tile needs to be cut off or added, you're employing the
kind of reasoning done in a Riemann sum.

Riemann sums (named after a 19th-century German mathematician)


are crucial to explaining integration in calculus, as tangible
introductions to the more precise fundamental theorem. A graph of a
Riemann sum showshow the area of a curve can be found by
building rectangles along the x, or horizontal axis, first up to the
curve, and then over it, and then averaging the distance between the
over- and underlap to get a more precise measurement.

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