Geometry problem in work of art

Sunday 12 April 2015

During the years 1795 to 1805 the famous English poet, printmaker and painter William Blake (1757-1827) created a color print entitled Newton, shown below.

The work of art depicts a naked Isaac Newton manipulating a geometer’s compass on a scroll of paper. Upon closer inspection of the scroll, one can clearly see a diagram that has what appears to be an equilateral triangle with an arc that intersects two of the triangle’s vertices. It also appears that a side of the triangle is tangent to the arc at each of the two lower vertices. This diagram (given the assumptions just made) poses an interesting geometry problem – which can be stated as follows (with some labeled points and shading added to the diagram):

Question: What fraction is the area of the shaded region (segment of a circle) of the area of the equilateral triangle DAB? (see diagram below right)

click on file name below to download this question and a full worked solution


The astrophysicist Mario Livi wrote an interesting article about this print called On Blake's 'Newton' which discusses Blake's resistance to the growing prominence of science and empiricism during the Enlightenment.  It turns out that Blake was not trying to compliment Newton and all that he represented in terms of science's progress in explaining natural phenomena - but, in fact, he was trying to do the contrary.

Tags: challenge, geometry


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