The tabletops in Crumble Coffee & Bakery on the southeast corner of 10th Street and College Avenue look like they’re made of old wood. The boards hint at a life before they were crafted into furniture, but after they were milled from timber.
The twice-over reclaimed character of the tabletops was confirmed by Crumble Coffee owner Scott Reynolds in an email to The Beacon. The wood was “first used in a hotel stables in Plainfield over a hundred years ago,” he wrote. After that, the wood was reclaimed for use in a barn in rural Monroe county. More recently, Reynolds said, “that barn wood was again reclaimed and refashioned into our tables.”
Among the hints that the wood is old are the kerf marks left by the circular saw that milled the wood.
How big was the saw? There’s enough information in the narrow boards to calculate the blade diameter. And that’s the problem for this edition of the Math Journal.
Feel free to write up your solution as a comment. If The Beacon has set up the commenting system correctly, your answer won’t spoil things for other people, because it will sit unseen, until it gets “approved.” After a month or so, any comments with correct answers will be approved. (If this website manages to turn a buck or two, maybe correct answers to future real-world math problems will be rewarded with some kind of prize. But it’s not there, yet.)
Kerf Mark Problem:
Assume the chord to the kerf-marked circle left by the saw blade measures 4 inches long and the distance from the mid-point of the chord to the kerf mark is 0.08278 inches.
What was the diameter of the saw blade that milled the timber for the piece of wood in the photo? (Show your work!)
Define a triangle with right angle at 6 on the ruler, and hypotenuse from 8 to the center of the saw blade. The hypotenuse is the radius (r), from 6 to the center is r – 0.08278, from 6 to 8 is 2, and since x^2 + y^2 = r^2 (Pythagorean Theorem), therefore
(r – 0.08278)^2 + (2)^2 = r^2,
r^2 – 2*r*0.08278 + (0.08278)^2 + 4 = r^2 — multiplying the squared terms
-2*r*0.08278 + (0.08278)^2 + 4 = 0 — subtract r^2 both sides
(0.08278)^2 + 4 = 2*r*0.08278 — add 2*r*0.08278 both sides
((0.08278)^2 + 4)/(2*0.08278) = r — divide both sides by 2*0.08278
24.2 = r, — calculator
The diameter of the saw blade is 48.4″.