Author Archives: Jim Stevenson

Lunchtime at the Fish Pond

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This is a problem from the 629 AD work of Bhaskara I, a contemporary of Brahmagupta.

“A fish is resting at the northeast corner of a rectangular pool. A heron standing at the northwest corner spies the fish. When the fish sees the heron looking at him he quickly swims towards the south (in a southwesterly direction rather than due south). When he reaches the south side of the pool, he has the unwelcome surprise of meeting the heron who has calmly walked due south along the side and turned at the southwest corner of the pool and proceeded due east, to arrive simultaneously with the fish on the south side. Given that the pool measures 12 units by 6 units, and that the heron walks as quickly as the fish swims, find the distance the fish swam.”

Answer.

See Lunchtime at the Fish Pond for a solution.

Stacked Rhombuses Puzzle

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This is a puzzle from Talwalkar’s set of “Impossible Puzzles with Surprising Solutions.”

“Call this puzzle the leaning tower of rhombi.

There are 5 isosceles triangles, aligned along their bases, with base lengths of 12, 13, 14, 15, 16 cm. The 10 quadrilaterals above are in rows of 4, 3, 2, and 1. Each quadrilateral is a rhombus, and the top of the tower is a square. What is the area of the square?”

Answer.

See Stacked Rhombuses Puzzle for solutions.

Evaporating Pool Problem

This is a fairly straight-forward problem from A+ Click.

“The water from an open swimming pool evaporates at a rate of 5 gallons per hour in the shade and 15 gallons per hour in the sun.  If the pool loses 8,400 gallons in June and there were no clouds, what is the average duration of night during that month?”

Answer Choices:     6 hours     8 hours     10 hours     12 hours

Answer.

See Evaporating Pool Problem for solutions.

Tom Lehrer New Math

I see another icon of the past has passed away: Tom Lehrer. Lehrer was a mathematician who put his talents to great use, in contrast with mathematicians like the neocon Paul Wolfowitz and Iraqi Ahmed Chalabi who helped foment the Iraq War.  He skewered all the shibboleths of the times (1950s and 60s) with his pre-politically-correct take-downs, mainly to the music of Gilbert and Sullivan.

Among his targets was the “New Math”—the Common Core of 60 years ago and a reminder that some things never change.  Fortunately, the New Math infiltrated public schools after my time, but you will recognize that its purpose is for students to understand math and not just perform rote manipulations.  A truly noble intent, but its continued reincarnation indicates how difficult it is to achieve.  So we are left with humor at our folly.

This video of “New Math” is from a live 1965 performance of “That Was the Year That Was”.  A more famous song is Lehrer’s musical rendition of the chemical periodic table, “The Elements” (performed live in 1967 in Denmark).  I invite you to listen to all his songs for an irreverent window into the past.

See “Tom Lehrer Dies at 97” for a PDF copy of his obituary.

Two Men Meet

This is another problem from the c.100AD Chinese mathematical work, Jiǔ zhāng suàn shù (The Nine Chapters on the Mathematical Art) found at the MAA Convergence website Convergence.

“A square walled city measures 10 li on each side.  At the center of each side is a gate.  Two persons start walking from the center of the city.  One walks out the south gate, the other the east gate.  The person walking south proceeds an unknown number of pu then turns northeast and continues past the corner of the city until they meet the eastward traveler.  The ratio of the speeds for the southward and eastward travelers is 5:3.  How many pu did each walk before they met? [1 li = 300 pu]”

Answer.

See Two Men Meet for a solution.

Railway Crossing Problem

This is an interesting problem from the 1966 Eureka magazine.

“A railway and a road run together for seven miles from P to Q. Two miles from P there is a level crossing, which is closed one minute before, and opened one minute after, a train passes.

A train passes a Stationary car at P and travels on to Q at 60 m.p.h., and, forgetting to slow down, crashes at Q; the car passes the train as it crashes. Assuming that stopping for an instant from full speed loses the car one minute, of what speed must it be capable?”

Answer

See the Railway Crossing Problem for a solution.

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