Who Needs Calculus?

In the dark ages before calculators, my farm-raised physicist dad had no practical use for calculus. To save time, he would plot data as a closed curves onto the same weight graph paper (important), with exact matching x and y axes marks/lengths (also important).

He would then grab scissors and cut out the curves, including the edge(s) of the x/y axis it included. He then had a smooth or lumpy — depending on the data — pancake or ice cream cone cut-out.

Next, he used scales (‘blind justice’ kind) to weigh each ice cream cone/pancake against a right triangle (cut-out from the same paper and same x/y axes). He knew the weight (he weighed it) and area of the triangle (H x W divided by 2).

If the scales balance, the area under the curve and the area of the triangle were the same. If the scales did not balance, weights (usually VERY small) were added to the lighter side until they did. Weights were tallied and simple algebra was scrawled out to solve.

So, the WEIGHT of the curve (WC) — compared to the weight and area of the triangle (WT and AT) — determined the AREA of the curve (AC).

WC/WT = AC/AT ….. AT*(WC/WT) = AC

i.e. IF WC = 4, WT = 2, AT=3, THEN AC = 6

Who needs Calculus?