While preparing a loosely related presentation, I recently tripped over a webpage featuring a turorial for finding the circumference of a circle. π * diameter was the simple formula, correct? Negative.
2πr
I was genuinely offended and wondered if I was just being fussy. The next time I saw my mechanic, 2πr hit the shop whiteboard. After a brief pause to parse the equation, he almost punched me in the throat while barking, "never do that!"
Then I saw the resident subject matter expert in early childhood development, with specific focus on education. It almost ended in me sleeping on the couch.
The Associative Property reminds us that factors in a multiplicative equation can be grouped in any order without changing the product. Not should. Certainly not must.
Pi times diameter is simple and easily internalized. As noted by my stalwart wrench, the diameter is usually known in practocal application to further bolster the forumula's memorization.
2πr can give people pause. It is unclear and does nothing to add implied commentary to its function. But proper use of the Associative Property away from laziness and toward clarity could be applied for the better.
2rπ
π(2r)
Utilize whitespace on the page to add a simple note about diameter. Anything but the unclear 2πr.
This little peeve of modern laziness went forgotten for a week until I casually thumbed through a book on my desk. The Great International Math on Keys Book, Rev. B by Texas Industries Learning Center.
This book was written to accompany the first widely-adopted pocket calculator with algebraic order of operations. Nearly fifty years ago.
*Insert profane indignance here*