We had two presentations and two mini-lectures today.

Mr Reihman gave an argument for his Conjecture D. We talked about how this is an “if and only if” statement, so it needs two proofs.

Then I spent some time discussing the axiomatic method.

Ms Carpenter shared work related to the second statement of Conjecture 1.1. In the end her result is:

*Theorem: (Carpenter)* Let ABCD be a square. Assume that the diagonals AC and BD
meet at a point X. Then angle BAC is congruent to angle BDC.

And I gave a pep talk about how

```
"Half a proof is no proof, but Progress is Progress."
```

Contact Prof Hitchman

Department of Mathematics 0506

University of Nothern Iowa

Cedar Falls, IA 50613-0506

Office: 327 Wright Hall

Phone: 319-273-2646

email: theron.hitchman@uni.edu