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1/4 + 1/16 + 1/64 + 1/256 + · · ·: Quiz


Question 1: A related construction making the figure similar to all three of its corner pieces produces the ________.
Sierpinski triangleChaos gameSierpinski carpetApollonian gasket

Question 2: The same strategy works for any finite ________.
Series (mathematics)ArchimedesCalculusGeometric series

Question 3: ________ encounters the series in his work Quadrature of the Parabola.

Question 4: More generally, for any a, the ________ whose first term is a and whose common ratio is 1/4 is convergent with the sum
Series (mathematics)Geometric seriesArchimedesCalculus

Question 5: He is finding the area inside a ________ by the method of exhaustion, and he gets a series of triangles; each stage of the construction adds an area 1/4 times the area of the previous stage.
EllipseConic sectionParabolaArchimedes

Question 6: The same geometric strategy also works for ________, as in the figure on the right:[2][5][6] if the large triangle has area 1, then the largest black triangle has area 1/4, and so on.


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