Geometric Models of Infinite Series

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4. Square ABCD has sides of length 1. Square EFGH is formed by connecting the midpoints of thesides of the first square, as shown in the figure. Assume that the pattern of shaded regions in thesquare is continued indefinitely. What is the total area of the shaded regions?It might help to complete the following table and then look for a pattern.Stepthe length ofa sidethe area of thesquare1 AB = 1 1the area of the triangle182EF = 2234
5. In the figure there are infinitely many circles approaching the vertices of an equilateral triangle, eachcircle touching other circles and sides of the triangle. If the triangle has sides of length 1, find thetotal area occupied by the circles.It might help to complete the following table and then look for a pattern.Steph, height of thetriangles, length of the sideof the triangles = 2 3 hr, radius of the A, area of the circlecircler = 3A = π r 26 s1 31 32 6π ⎜ ⎛ 3⎝ ⎠ ⎟⎞26 234
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Page 3: 3. To construct thesnowflake curve

Geometric Models of Infinite Series

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