Jan 11, 2017: Rhombi, part 1

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We briefly discussed the process behind writing for the class journal.

Ms Lewis took up challenge 1.4. She presented a construction, and a proof that it works, and then we all practiced writing out the statement of the theorem. In the end, we had this:

Theorem: [Lewis] Given a segment AB, one can construct a rhombus ABCD using a compass and straightedge.

If you have an alternate method for this theorem, or any other, please consider presenting it. We can learn a lot from having and comparing multiple methods.

Then Ms Maass took on Conjecture 1.6. The argument hinged on using Euclid’s Proposition I.34, which we all found confusing. After discussion, we decided that it has the hypotheses and conclusions the wrong way around for what Ms Maass needed. (In technical terms, Ms Maass needs the converse to I.34 for her argument.)

Finally, Ms Carpenter took up 1.2. After some discussion, we decided that this argument is unconvincing because it doesn’t directly use the definition of “meet” for two segments.

And we talked a little bit about how Euclid was mean to us and didn’t actually define the term parallelogram. But we sorted out what we want.

I am very pleased with the progress and work so far. Keep at it!