This is a stimulating little problem from the ever-creative James Tanton:
“An ant is at the east end of an infinite stretchy band, initially 2 ft long. Each day: ant walks 1 ft west on the band. Overnight while sleeping, band stretches to double its length (carrying ant westward as does so). Same routine each day/night. Will ant cover 99% of band’s length?”
(Ant from clipart-library.com)
See the Rubber Band Ant
Given the aggravating times, I thought I would vent my frustration by ranting on a somewhat nonsensical topic: “The fact that the earth revolves around the sun, rather than the sun around the earth.” This assertion is often used to separate the supposed dunces from the enlightened. It is put on the same level as “the fact that the earth is round (a sphere) and not flat” with the dunces labeled “flat-earthers.”
However, I take umbrage with the use of the word “fact” to conflate these two instances as examples of what “is” or what is “true.” I claim the earth is spherical (more or less: a better approximation is an oblate spheroid) or certainly “curved” rather than “flat.” Whereas the statement that the “sun is at the center of the solar system” is not a fact but an arbitrary convenience.
See Meditation on “Is” in Mathematics III – Heliocentrism
Given the mathematical nature of this website I feel reluctantly impelled to address the coronavirus pandemic. The mathematics behind the spread of infection is basically the same exponential growth that I discussed in the “Math and Religion” post and has recently been explained by the ever-lucid Grant Sanderson at his 3Blue1Brown website.
What I wish to draw attention to is the series of posts on the coronavirus by Kevin Drum on his website at Mother Jones. I have collected his recent posts comparing the spread of the virus in various countries and added some mathematical commentary of my own, which is the content of this post.
But the bottom line seems to be that in virtually all the countries, including the US, the virus infection is spreading at the Italian rate of doubling every 4 days! The readers of this website are sufficiently numerate to realize the frightening import of that number. If that weren’t enough, Kevin provides additional posts on the results of the modeling at the Imperial College that are truly nerve-wracking for someone such as myself in the most vulnerable cohort. The only blessing so far seems to be that, for once, the children are spared.
At this time, I don’t have the stomach to keep updating the post as new numbers come in. That may change. I could address the catastrophe of having ignorance and incompetence at the helm of the national ship of state, but it is too depressing.
See the Coronavirus Mathematics
(Update 3/17/2020, Update 3/21/2020, Update 4/17/2020, Update 9/20/2020) Continue reading
This is another problem from the indefatigable Presh Talwalkar.
_ _____Hard Geometry Problem
“In triangle ABC above, angle A is bisected into two 60° angles. If AD = 100, and AB = 2(AC), what is the length of BC?”
See Hard Geometric Problem
(Update 7/18/2020, 7/20/2020) Alternative Solution Continue reading
Having fallen under the spell of Catriona Shearer’s geometric puzzles again, I thought I would present the latest group assembled by Ben Orlin, which he dubs “Felt Tip Geometry”, along with a bonus of two more recent ones that caught my fancy as being fine examples of Shearer’s laconic style. Orlin added his own names to the four he assembled and I added names to my two, again ordered from easier to harder.
See Geometric Puzzle Munificence.
(Update 4/16/2020) Ben Orlin has another set of Catriona Shearer puzzles 11 Geometry Puzzles That Drive Mathematicians to Madness which I will leave you to see and enjoy. But I wanted to emphasize some observations he included that I think are spot on. Continue reading