Circumparabolic Regions Inside a Unit Circle

circumparabolic regions

A circumparabolic region is found between a circle and a parabola, with the circle being chosen to include the vertex and x-intercepts of the parabola used, with the circle, to define the two circumparabolic regions for a given parabola-circle pair. There are four such regions shown above, rather than only two, because two parabolas are used above. The formulae for the parabolas, as well as the circle, are shown.

A puzzle which I will not be solving, I suspect, until I learn more integral calculus: what fraction of the circle’s area is shown in yellow?

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10 Responses to Circumparabolic Regions Inside a Unit Circle

  1. goobypl5 says:

    So the answer is approx 15% (I won’t spoil the exact one). Do you know of a proof that does not require integration?

    Liked by 1 person

  2. ejohn152 says:

    The yellow area is pi minus eight thirds of square unit.

    This approx. = 0.47492

    Archimedes of Syracuse needed no calculus. RSVP

    ________________________________

    Liked by 1 person

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