Answers to problems in this issue

Mombe Magic - page .

This is your wise solution: First, you borrow a cow from a neighbour. Then there will be 18 cows, so you give half (9) to the eldest son, one third (6) to the next son, and one ninth (2) to the youngest son. There will still be one cow left, which you can now return to the neighbour!

Solutions to Thales Problems on page

1. By the sine law, d = [(lsina)/(sing)] = [(lsina)/(sin(90-a-b))] = [(lsina)/(cos(a+b))].
2. If you construct, on the sand, a triangle P¢Q¢R¢ similar to the big one PQR, using the measured angles, then you can use simple proportionality to calculate d = PR, because you can measure P¢R¢ and Q¢R¢ in the sand and QR in the air, using your string (and any units).
3. Set your hinged rulers to the angle q whose tangent is 2, by constructing in the sand the right triangle shown in the diagram. Now walk along the shoreline until the angle ÐABC the shoreline makes with the direction to the ship is q, and mark the spot (B). Next, walk back along the shoreline in the other direction until the angle ÐACB between ship and shoreline is again q. Mark this spot (C). The distance to the ship is the distance BC you walked. Can you see why?

Goethe
``It has been said that figures rule the world. Maybe. But I am sure that figures show us whether it is being ruled well or badly.'' In J. P. Eckermann, Conversations with Goethe.

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On 14 Jan 2001, 09:58.