The Austrian mathematician Georg Pick has two claims to fame. One is that he was a close friend of Albert Einstein and proved instrumental in bringing the young scientist to the German University in Prague in 1911. The other is that he wrote a short paper, published in 1899, on ‘reticular’ geometry. From a lifelong
work covering a wide range of topics he is remembered for the captivating Pick’s theorem – and what a theorem it is!
Pick’s theorem gives a means for computing the area enclosed by a manysided (or polygonal) shape formed by joining up points whose coordinates are whole numbers. This is pinball mathematics.
To find the area of the shape we shall have to count the number of points • on the boundary and the number of interior points o. In our example, the number of points on the boundary is b = 22 and the number of interior points is c = 7. This is all we need to use Pick’s theorem:
From this formula, the area is 22/2 + 7 – 1 = 17. The area is 17 square units.
It is as simple as that. Pick’s theorem can be applied to any shape which joins discrete points with whole number coordinates, the only condition being that the boundary does not cross itself.
work covering a wide range of topics he is remembered for the captivating Pick’s theorem – and what a theorem it is!
Pick’s theorem gives a means for computing the area enclosed by a manysided (or polygonal) shape formed by joining up points whose coordinates are whole numbers. This is pinball mathematics.
To find the area of the shape we shall have to count the number of points • on the boundary and the number of interior points o. In our example, the number of points on the boundary is b = 22 and the number of interior points is c = 7. This is all we need to use Pick’s theorem:
From this formula, the area is 22/2 + 7 – 1 = 17. The area is 17 square units.
It is as simple as that. Pick’s theorem can be applied to any shape which joins discrete points with whole number coordinates, the only condition being that the boundary does not cross itself.
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