The Tippe Top

The tippe top is a round top that, when spun, tilts to one side and leaps up onto its stem. This is perplexing, as the toy appears to be gaining energy — its center of mass rises with the flip.

How is this possible? The geometrical center of the top is higher than its center of mass. As the toy begins to topple to one side, friction with the underlying surface produces a torque that kicks it up onto its stem. It does gain potential energy, but it loses kinetic energy — in fact, during the inversion it actually reverses its direction of rotation.

Entire treatises have been written on the underlying physics, and the toy has occupied at least two Nobel Prize winners — below, Wolfgang Pauli and Niels Bohr play with one at the inauguration of the Institute of Physics at Lund, Sweden, in July 1954.


German astronomer Karl Reinmuth discovered and named more than 400 asteroids. Among them are these eight:

1227 Geranium
1228 Scabiosa
1229 Tilia
1230 Riceia
1231 Auricula
1232 Cortusa
1233 Kobresia
1234 Elyna

Their initials spell G. STRACKE, for Gustav Stracke, a fellow astronomer who had asked that no planet be named after him. In this way Reinmuth could honor his colleague without contradicting his wish.


Astronaut John Young smuggled a corned beef sandwich into space. As Gemini 3 was circling Earth in March 1965, Young pulled the sandwich out of his pocket and offered it to Gus Grissom:

Grissom: What is it?

Young: Corned beef sandwich.

Grissom: Where did that come from?

Young: I brought it with me. Let’s see how it tastes. Smells, doesn’t it?

Grissom: Yes, it’s breaking up. I’m going to stick it in my pocket.

Young: Is it? It was a thought, anyway.

“Wally Schirra had the sandwich made up at a restaurant at Cocoa Beach a couple of days before, and I hid it in a pocket of my space suit,” Young explained later. “Gus had been bored by the official menus we’d practiced with in training, and it seemed like a fun idea at the time.”

Grissom wrote, “After the flight our superiors at NASA let us know in no uncertain terms that non-man-rated corned beef sandwiches were out for future space missions. But John’s deadpan offer of this strictly non-regulation goodie remains one of the highlights of our flight for me.”


  • Colombia is the only South American country that borders both the Atlantic and the Pacific.
  • 28671 = (2 / 8)-6 × 7 – 1
  • Can a man released from prison be called a freeee?
  • “Nature uses as little as possible of anything.” — Johannes Kepler

Sergei Prokofiev died on the same day that Joseph Stalin’s death was announced. Moscow was so thronged with mourners that three days passed before the composer’s body could be removed for a funeral service.

(Thanks, Alina.)

The Indiana Pi Bill

In 1894, Indiana physician Edwin J. Goodwin published a one-page article in the American Mathematical Monthly claiming to have found a method of squaring the circle — that is, of constructing a square with the same area as a given circle using only a compass and straightedge, a task known to be impossible. He proposed a bill to state representative Taylor I. Record, laying out the “new mathematical truth” and offering it “as a contribution to education to be used only by the State of Indiana free of cost by paying any royalties whatever on the same, provided it is accepted and adopted by the official action of the legislature of 1897.”

Apparently flummoxed, the House referred the bill to its Committee on Swamp Lands, which transferred it to the Committee on Education … which approved it. Whereupon the whole house passed it unanimously.

The bill, which the Indianapolis Journal was already calling “the strangest bill that has ever passed an Indiana Assembly,” moved on to the senate, which referred it the Committee on Temperance. (Chronicler Will E. Edington writes, “One wonders whether this was done intentionally, for certainly the bill could have been referred to no committee more appropriately named.”) Equally flummoxed, the committee recommended that it pass.

The bill might have achieved full passage had not Purdue mathematics professor C.A. Waldo happened to be visiting the House that day. “A member … showed the writer a copy of the bill just passed and asked him if he would like an introduction to the learned doctor,” Waldo later recalled in the Proceedings of the Indiana Academy of Science. “He declined the courtesy with thanks, remarking that he was acquainted with as many crazy people as he cared to know.”

That did it. “Representative Record’s mathematical bill legalizing a formula for squaring the circle was brought up and made fun of,” reported by Indianapolis News on Feb. 13. “The Senators made bad puns about it, ridiculed it and laughed over it. The fun lasted half an hour. Senator Hubbell said that it was not meet for the Senate, which was costing the State $250 a day, to waste its time in such frivolity.”

“Senator Hubbell characterized the bill as utter folly,” added the Indianapolis Journal. “The Senate might as well try to legislate water to run up hill as to establish mathematical truth by law.”

Round and Round

In describing a large water basin, 2 Chronicles 4:2 reads, “Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.” A similar verse appears at 1 Kings 7:23.

Critics point out that this implies that π is 3, and in 1983 about 100 professors and students at Emporia State University in Kansas founded an Institute of Pi Research to lobby (wryly) for adopting this new value in place of the awkward 3.14159 …

“To think that God in his infinite wisdom would create something as messy as this is a monstrous thought,” medieval historian Samuel Dicks told the Kansas City Times. “I think we deserve to be taken as seriously as the creationists.”

“If the Bible is right in biology, it’s right in math,” added economic historian Loren Pennington.

But writing in the Mathematical Gazette in 1985, M.D. Stern of Manchester Polytechnic noted (also wryly) that the word translated as line above is transliterated qwh but read qw. Further, the ancient Greeks and Jews used letters to denote numbers, with the letters q, w, and h taking the numerical values 100, 6, and 5.

“Thus the word translated line in its written form has numerical value 111 whereas as read the value is 106. If we take the ratio of these numbers as a correcting factor for the apparent value of π as 3 and calculate 3 × (111/106), we obtain 3.141509 to 7 significant figures. This differs from the true value of π by less than 10-4 which is remarkable. In view of this, it might be suggested that this peculiar spelling is of more significance than a cursory reading might have suggested.”