Misc

  • The newsletter of the Procrastinators’ Club of America is called Last Month’s Newsletter.
  • Samuel Johnson’s 1755 Dictionary defines dross as “the recrement or despumation of metals.”
  • A sphere of radius n kilometers has almost exactly the same volume as a cube of side n miles. (Randall Munroe)
  • Cookie Monster’s real name is Sid.
  • “Henry James chews more than he bites off.” — Clover Adams

“There exist only two kinds of modern mathematics books: ones which you cannot read beyond the first page and ones which you cannot read beyond the first sentence.” — Physics Nobelist Yang Chen-Ning

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Ghost Tint

https://commons.wikimedia.org/wiki/File:Neon_Color_Circle.gif
Image: Wikimedia Commons

There’s no blue circle here. The space among the lines is white. In the presence of black lines, the hue of a colored object seems to bleed into the surrounding background.

The phenomenon was first discovered in 1971. It’s known as neon color spreading.

| Oddities · Science & Math

The Oppel–Kundt Illusion

https://commons.wikimedia.org/wiki/File:Fig_OK.tif
Image: Wikimedia Commons

A segment of an image tends to seem larger when it’s filled with visual elements. This is true whether the elements are discrete or continuous.

Above, the right part of the top figure and the left part of the bottom figure each seems to fill more than half of its tier, though plainly these impressions can’t both be valid.

The illusion was first studied by German physicists Johann Joseph Oppel and August Kundt in the 1860s.

| Science & Math

The Koffka Ring

https://commons.wikimedia.org/wiki/File:Koffka-Ring_1.svg
Image: Wikimedia Commons

In all three of these figures, the gray ring’s color is uniform. But in the second and third figures the upper half appears distinctly darker, showing that the brain exaggerates differences in brightness between adjacent surfaces. German psychologist Kurt Koffka first reported the effect in 1935.

| Science & Math

Happy Returns

Famously, in a group of 23 randomly chosen people, the chance is slightly higher than 50 percent that two will share a birthday.

Here’s an interesting variant: If the group consists of an equal number of girls and boys, what’s the minimum size at which it’s probable that a girl and a boy share a birthday?

Surprisingly, the answer is only 32 (16 girls and 16 boys). If we want a girl and a boy to share the same birth month, we need only 6 children before this becomes probable.

(Tony Crilly and Shekhar Nandy, “The Birthday Problem for Boys and Girls,” Mathematical Gazette 71:455 [March 1987], 19-22. See Shared Birthdays.)

| Science & Math

Roman Surprise

What’s the largest number that can be expressed in Roman numerals? If no single letter can appear more than three times in a row, then the highest we can go is 3,999, or MMMCMXCIX.

These 3,999 values contain in total 30,000 characters, and, pleasingly, reader Ian Duff finds that 5,600 are Is, 2,000 are Vs, 6,000 are Xs, 2,000 are Ls, 6,000 are Cs, 2,000 are Ds, and 6,400 are Ms.

(Thanks, Ian.)

| Science & Math · Trivia