Pyhtagoras Vs My Husband...

A few days ago we were hanging a picture, salvaged from a garage sale, on our living room wall.  This picture was purchased by my retro-loving husband on the way from the beach to our friends' house on the Cape Cod. When the friend asked him how much this monster costs, my husband replied: "two-fifty."  The friend then cautiosly looked at him and said: "You know, Moshe, two hundred and fifty dollars is a lot of money for a textile print."  "No, this was two dollars and fifty cents,"  my husband triumphantly replied.

We had just a perfect wall for it.  My dear husband, who rarely applies his perfectionism to household chores, proudly demonstrated to me on this occasion that he was using a level to ensure it hang straight. However, as soon as the last nail went into the wall, it became obvious the picture was skewed towards the nearby corner.

This contradiction dazzled us – shall we trust what we see or what we measure? Do I side with my husband and his brand new set of Home Depot tools? Can I just avert my eyes from this giant, misaligned 1970's piece of artwork in the middle of my living room, or shall I fight for the visual re-adjustment that would contradict the laws of gravity? Uncomfortable with either option, I continued to investigate and soon realized that an imperfection must be the answer to this puzzle. Either one of our house walls was not vertical, or the picture we hung was not a perfect rectangle. Both options were not very attractive, but at least they kept the peace in our household and maintained the laws of nature.

Now it was a matter of measuring the picture corners. This could be done with a simple rectangular sheet of paper or a measuring tape. Remember the Pythagorean Theorem?  We frequently forget that its converse is also true, and in any triangle if its sides fit the equation x² + y² = z² then the angle between sides x and y is 90 degrees.

To be honest, I am afraid to perform this measurement. What if our house wall is not straight? Imagine how many new mathematical problems this can generate.