Discovering the Golden Hexagon
on Day 168 of a Leap Year.

Today we looked at the calendar and realised it was June 16. We remembered that the year 2000 was a leap year and that in leap years February has one more day than in normal years. We calculated that it was day 168 of the year, the same number as our school.

Next we explored how circular objects such as coins or plates can be fitted together in different ways so as to make interesting patterns. We investigated using discs of paper how coins could be arranged in lines (rows), columns and squares, and also in triangles and hexagons. If we make a triangle starting with a row of coins, each new row contains one less coin.

We showed ourselves how 6 similar paper discs could fit exactly around another disc and how this could also be done with plates. We learnt how with coins the pattern had been called Hesterīs Rose and how if we had more discs we could build larger patterns.

Golden Hexagon of Patagonia made out of 169 Argentina coins (10 centavo) with corresponding 169 square Click photo to enlarge (77K)

We saw how 169, golden coloured 10 centavo coins can be arranged exactly in the shape of a square and also in the shape of a hexagon - the Golden Hexagon of Patagonia.

We realised if the central coin from the square or hexagon was removed we could obtain a square or hexagon with a hole in the middle, and both of them would contain exactly 168 coins.

We had found in our School 168 on day 168 of the year, how interesting 168 coins could be. Tomorrow will be June 17 and day 169. Of course next year is not a leap year so 2001 June 17 will not be day 169 but 168. What other interesting things will be found out about 168 or 169 by then? - learning notes

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