Lights on the Geometree?

The day after the great "American Feast", known as Thanksgiving, Mr. Rivard and his 3 dedicated students, went to work on the actual artificial tree that is now known as the “Geometree”. It fit nicely in the corner of the classroom for all to see. But the problem to be determined was, ‘How Many Strings of Lights’ will be needed for the tree to appear festive right from the start? (See Figure A above)

A.   The number of lights on the Geometree was found by using a formula for Cone and Similar Triangles. “In Euclidean geometry the loci studied after lines and planes are usually the conic sections in plane geometry and the quadric surfaces in solid geometry. This is true even in secondary school geometry where we usually confine ourselves to the particular conics or quadrics known as circles and spheres, respectively. From the analytic point of view the conics follow naturally after the study of lines since they are the loci having second-degree equation.” W.T. Fishback, Projective and Euclidean Geometry.

Practically: solving the problem of ‘How Many Strings of Lights’ could save you and your family money in the long run.You may be able to stay in your Holiday Budget.

I invite the students or Mr. Rivard to share the formula that they used in the comment section below, so we can all plan a budget for the proper number of lights on our tree next year.

Next post will be about the lights on B. GEE.ARTISTREE.

Comments

[exoptica]

So how long will this continue? Every day until the New Year 2011, and beyond.

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I thank thee that I am none of the wheels of power but I am one with the living creatures that are crushed by it.