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.


  1. Having seen similar issues in our house, I would go with the walls not being perfectly vertical... but at least they are relatively sturdy.

  2. Oh yeh! We are spoiled in USA, as so many of our rooms are Nearly Rectangular, we think they certainly are. Elsewhere in much of the world, of course, there is less assumption of that standard.

    Where we are renting now in Tucson AZ, many of our rooftops are flat since there is virtually never any snow. I should say Nearly Flat, for there is some rain, so there should usually be some slight slope, and there is. While the ceilings COULD still be horizontal, in fact many of our ceilings reflect the slope of the roof. A really vaulted ceiling would not be annoying, but the slightly nonflat ceiling can make picture hanging difficult.

    Maria's right, everywhere there are walls that are not vertical, and floors that are not rectangular. THAT is one of the laws of nature.

  3. You could use the level to solve the problem rather than measuring and using the Pythagorean Theorem. Here's how: once the top plane of the picture is level, gently push on the picture to keep it in place, then put the level along a side of the picture. If both sides of the picture are 90 degrees to the floor, the wall is crooked. Or, you could put the level up against the wall and check its plum. If you don't intend to slap a vice on the diagonals of the picture and straighten it, and don't intend to re-plaster or re-stud your wall, adjust the picture in a way that is visually appealing without using the level, or draw confusing patterns on the wall between the picture and the corner.

  4. 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.

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