Math for Hanging Pictures

This blog is about using elementary math in our daily lives as adults. Here's a practical example.

I bought three old icons and I want to hang them above a small fireplace mantle. Unlike many of my simple hanging projects I can't just bang a nail in the middle of the wall then move it around to get things straight. Here are the issues:

• The wall is made of brick so holes have to be drilled for hangers
• I want my 3 items to hang at the same height and to be evenly spaced
• The three pictures are slightly differing sizes and are not "square"
• The pictures already have hangers on their backs which I don't want to move
• The hangers are not in exactly the same position on the backs

For you visual learners, here is an illustration of the situation:

• I need to know the sizes of the 3 icons (they are almost the same, I learned).
• I need to know the width of the mantle - is it wide enough that the three will fit with appropriate spacing between them? (yes)
• I need to decide on the height of the icons above the mantle. I think an inch or two is okay.
• I need to know the drop from the top of the icon to the wire, to know where to drill into the wall.

Let's call the icons A, B and C and the mantle M and the hook locations HA, HB, HC.
We'll worry about the horizontal spacing first.

Is   Mwidth - (Awidth + Bwidth + Cwidth) greater than 0?   Yes. The answer is 7 inches, therefore

    A + 3.5 + B + 3.5 + C = M           

This means the horizontal hook spacing will be, starting from the left edge of the mantle,

    HA = Awidth ÷2

and starting from the right edge of the mantle,

    HC = Cwidth ÷2

and finally, a hook for the last icon is
                              
    HB = HA + (Awidth ÷2) + 3.5" + (Bwidth ÷2)

or to be safer, just put it in the middle of the other two hangers

    HB = (distance between HA to HC ÷ 2)

The vertical position is calculated like this -

The icons are 12" tall, subtract 2" inches drop to get 10 inches then add 1" for clearance at the bottom.

If I put the hangers 11" above the mantle the icons should be at the right height.

Of course, on a brick wall it's difficult because I'd prefer to drill into the mortar rather than the bricks. I had to put the icons slightly lower, but not touching the shelf, so my holes went into mortar.

Here's how it came out: