Sources page biographical material

6.Y. ROPE ROUND THE EARTH
The first few examples illustrate what must be the origin of the idea in more straightforward situations.
Lucca 1754. c1330. F. 8r, pp. 31 32. This mentions the fact that a circumference increases by 44/7 times the increase in the radius.

Muscarello. 1478.

Ff. 932-93v, p. 220. A circular garden has outer circumference 150 and the wall is 3½ thick. What is the inner circumference? Takes π as 22/7.

F. 95r, p. 222. The internal circumference of a tower is 20 and its wall is 3 thick. What is the outer circumference? Again takes π as 22/7.

Pacioli. Summa. 1494. Part II, f. 55r, prob. 33. Florence is 5 miles around the inside. The wall is 3½ braccia wide and the ditch is 14 braccia wide -- how far is it around the outside? Several other similar problems.

William Whiston. Edition of Euclid, 1702. Book 3, Prop. 37, Schol. (3.). ??NYS -- cited by "A Lover" and Jackson, below.

"A Lover of the Mathematics." A Mathematical Miscellany in Four Parts. 2nd ed., S. Fuller, Dublin, 1735. The First Part is: An Essay towards the Probable Solution of the Forty five Surprising PARADOXES, in GORDON's Geography, so the following must have appeared in Gordon. Part I, no. 73, p. 56. "'Tis certainly Matter of Fact, that three certain Travellers went a Journey, in which, Tho' their Heads travelled full twelve Yards more than their Feet, yet they all return'd alive, with their Heads on."

Carlile. Collection. 1793. Prob. XXV, p. 17. Two men travel, one upright, the other standing on his head. Who "sails farthest"? Basically he compares the distance travelled by the head and the feet of the first man. He notes that this argument also applies to a horse working a mill by walking in a circle; the outside of the horse travels about six times the thickness of the horse further than the inside on each turn.

Jackson. Rational Amusement. 1821. Geographical Paradoxes, no. 54, pp. 46 & 115-116. "It is a matter of fact, that three certain travellers went on a journey, in which their heads travelled full twelve yards more than their feet; and yet, they all returned alive with their heads on." Solution says this is discussed in Whiston's Euclid, Book 3, Prop. 37, Schol. (3.). [This first appeared in 1702.]

K. S. Viwanatha Sastri. Reminiscences of my esteemed tutor. In: P. K. Srinivasan, ed.; Ramanujan Memorial Volumes: 1: Ramanujan -- Letters and Reminiscences; 2: Ramanujan -- An Inspiration; Muthialpet High School, Number Friends Society, Old Boys' Committee, Madras, 1968. Vol. 1, pp. 89-93. On p. 93, he relates that this was a favourite problem of his tutor, Srinivasan Ramanujan. Though not clearly dated, this seems likely to be c1908-1910, but may have been up to 1914. "Suppose we prepare a belt round the equator of the earth, the belt being 2π feet longer, and if we put the belt round the earth, how high will it stand? The belt will stand 1 foot high, a substantial height."

Dudeney. The paradox party. Strand Mag. 38 (No. 228) (Dec 1909) 673 674 (= AM, p. 139).

Anon. Prob. 58. Hobbies 30 (No. 773) (6 Aug 1910) 405 & (No. 776) (27 Aug 1910) 448. Double track circular railway, five miles long. Move all rails outward one foot. How much more material is needed? Solution notes the answer is independent of the length.

Ludwig Wittgenstein was fascinated by the problem and used to pose it to students. Most students felt that adding a yard to the rope would raise it from the earth by a negligible amount -- which it is, in relation to the size of the earth, but not in relation to the yard. See: John Lenihan; Science in Focus; Blackie, 1975, p. 39.

Ernest K. Chapin. Loc. cit. in 5.D.1. 1927. Prob. 5, p. 87 & Answers p. 7. A yard is added to a band around the earth. Can you raise it 5 inches? Answer notes the size of the earth is immaterial.

Collins. Book of Puzzles. 1927. The globetrotter's puzzle, pp. 68 69. If you walk around the equator, how much farther does your head go?

Abraham. 1933. Prob. 33 -- A ring round the earth, pp. 12 & 24 (9 & 112).

Perelman. FMP. c1935?? Along the equator, pp. 342 & 349. Same as Collins.

Sullivan. Unusual. 1943.

Prob. 20: A global readjustment. Take a wire around the earth and insert an extra 40 ft into it -- how high up will it be?

Prob. 23: Getting ahead. If you walk around the earth, how much further does your head go than your feet?

W. A. Bagley. Puzzle Pie. Op. cit. in 5.D.5. 1944. Things are seldom what they seem -- No. 42a, 43, 44, pp. 50-51. 42a and 43 ask how much the radius increases for a yard gain of circumference. No. 44 asks if we add a yard to a rope around the earth and then tauten it by pulling outward at one point, how far will that point be above the earth's surface?

Richard I Hess. Puzzles from Around the World. The author, 1997. (This is a collection of 117 puzzles which he published in Logigram, the newsletter of Logicon, in 1984-1994, drawn from many sources. With solutions.) Prob. 28. Consider a building 125 ft wide and a rubber band stretched around the earth. If the rubber band has to stretch an extra 10 cm to fit over the building, how tall is the building? He takes the earth's radius as 20,902,851 ft. He gets three trigonometric equations and uses iteration to obtain 85.763515... ft.

Erwin Brecher & Mike Gerrard. Challenging Science Puzzles. Sterling, 1997. [Reprinted by Goodwill Publishing House, New Delhi, India, nd [bought in early 2000]]. Pp. 38-39 & 77. The M25 is a large ring road around London. A man commutes from the south to the north and finds the distance is the same if goes by the east or the west, so he normally goes to the east in the morning and to the west in the evening. Recalling that the English drive on the left, he realised that his right wheels were on the outside in both journeys and he worried that they were wear out sooner. So he changed and drove both ways by the east. But he then worried whether the wear on the tires was the same since the evening trip was on the outer lanes of the Motorway.