“To most outsiders, modern mathematics is unknown territory… a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.”
— Ivars Peterson, Mathematical Association of America
I don’t really love math. If I did, I wouldn’t have spent so much time in my youth trying to learn to play “Hideaway” note-for-note on the guitar like Freddy King. Nor would I have spent countless hours watching Gilligan try to get off the island on television. I don’t love math any more than I love grammar or diagramming sentences, but I do love to write, so I do my best to understand them in order to perfect the craft.
By the same token, I love to design lighting systems, so I do my best to understand certain mathematical relationships so that I can perfect the craft. My biggest fear is that one day I’ll walk on site at a project where I designed the lighting and find that there’s not enough illuminance, the angle of projection is too high, or the field width of the luminaires isn’t wide enough to cover the stage uniformly. These are real world scenarios where a good grasp of just a few mathematical relationships can help prevent lighting catastrophes. I have recurring nightmares about those things, second only to my “stuck out in public nude” nightmares and my “missed a final exam” nightmares.
So I love math to the extent that I have a real desire to figure out the world around me, to figure out what makes it tick, and how to dismantle it in case the ticking is that of a time bomb. And I’ve found that you don’t have to be Albert Einstein or Gottfried Leibniz to figure out enough to be proficient in the design of lighting systems. Actually, there are only a handful of things to know about math that will help you perfect the craft of lighting. If you’re like me and your brain can only hold so much, make sure it’s holding these five things:
5. Units of measure unlock hours of pleasure — The units of measure can give you strong hints about how to figure out math problems. For example, if you’re trying to figure out how much energy a light uses, then the units of measure tell you to multiply the number of watts by the numbers of hours the light was on. And if the time is given in minutes instead of hours, then look to the units of measure to convert from one to the other. There are sixty minutes in one hour, so if you divide the number of minutes by sixty, you’ll come away with hours. Why? The units of measure are: minutes divided by minutes per hour = hours.
4. Even it up — If you have an equation with the value you’re looking for but it’s on the wrong side, you can manipulate it to make it yield that value which you are looking for. Just make sure that whatever you do to one side of an equation, do the same to the other side; then you haven’t changed the relationship. For example, if you know that
V = I x R (Ohm’s law!)
but you want to figure out I or R instead of V, then you can divide both sides by I or R to change the equation:
3. If it ain’t right, it’s wrong — A right triangle is one in which there is a 90° angle. Right triangles are user friendly because we know a lot about the relationships between the lengths of the sides and the three angles in a right triangle. If we can identify a right triangle and we know the length of two sides, two angles (one of which is 90°), or one side and one angle, then we can find out the length of all three sides and all three angles. The good thing is that any triangle can be turned into two right triangles (if it isn’t already a right triangle) by drawing a perpendicular line from the apex of one angle to the opposite side.
2. Pythagoras had a theorem — Some dude who lived long before Christ recognized that there was a fixed relationship between the lengths of the sides of a right triangle. That relationship, called the Pythagorean Theorem, simply says that the square of one side – the side opposite the right angle – is the same as the sum of the squares of the other two sides. In equation form it looks like this:
a2 = b2 + c2
So if you know the length of any two sides in a right triangle, you can figure out the length of the third.
1. Sines of the times — Learning a little trigonometry will take you a long way. It’s not as difficult as figuring out how to play “Hideaway” like Freddy King. It’s simply plugging in two values of a right triangle to figure out the unknown third value. It looks like this:
Sinθ = opposite side ÷ hypotenuse
where θ is the angle and the hypotenuse is the side opposite the right angle. Don’t let the terms “trig” or “hypotenuse” frighten you. They’re actually very simple concepts.
Stephen Hawking was once told by his publisher that his book sales would halve for every math equation he put in. From my experience leading seminars, I know that many of us in the industry loves math about as much as the lighting crew s those obnoxious sound checks. But as a product of the Texas public school system, I’m here to tell you — if I can figure this stuff out, certainly you can.
If you find math difficult to stomach, then do what my daughter does when she has to take her vitamins — hold your nose and just do it. It’ll build strong bones and muscles in the weakest of math minds.
