Explore BrainMass

Explore BrainMass

    Proof by Mathematical Induction : Planes, Lines and Regions

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Suppose that n straight lines in the plane are positioned so that no two are parallel an no three pass throught the same point. Show that they divide the plane into 1/2(n^2 + n + 2) distinct regions.

    © BrainMass Inc. brainmass.com February 24, 2021, 2:18 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/proof-mathematical-induction-planes-lines-regions-12807

    Solution Preview

    First we prove that how many distinct regions will be created if the n+1th line show up in the plane where there are n lines exist already.

    That's will be easy to find that there will be n+1 distint regions created if the n+1th line show ...

    Solution Summary

    A proof linking lines, planes and regions is provided.

    $2.19

    ADVERTISEMENT