Legos, by the numbers, stack up perfectly

People often have favorite colors or words or names or songs or cars. But they seem to seldom have favorite numbers.

In fact, I tested this idea with a class and found that most people did not think numbers were important enough to be given favored status.

If they had such a number, it was considered a lucky number because of its relationship to some emotional event or object.

I think some of my favorite numbers are eight, 16, 24, 40, six-fifths and one-third. This is because these represent proportions in the world of Lego engineering.

As such, they can be used to build significant objects and to engage student minds. Most expert builders with Legos are under 12 years old and are unaware that Legos are constructed with their own engineering standards.

If you are new to the world of Lego construction, you need to know some terminology so you can follow the discussion. The rounded protrusions that fit into the bottom of other pieces are called studs. Lego pieces with a single row of studs are called beams.

If there are two rows of studs, they are called bricks, and if there are more than two rows, they are called plates.

The bricks, beams and plates are further distinguished by the number of studs — there being eight stud bricks, 10 stud bricks, four stud beams, etc. That’s enough for now.

Lego bricks have a vertical unit that is six-fifths the horizontal unit. That is, a stack of five bricks is the same height as the length of a six-stud beam.

This is helpful when you are trying to build a complex structure. If you build structures with vertical heights equal to horizontal lengths, you can utilize braces.

Plates, on the other hand, are one-third the height of a brick (or beam) so it takes three plates to raise a level one brick.

Lego gears are always differentiated by the number of teeth. They come in four sizes: eight teeth, 16 teeth, 24 teeth and 40 teeth.

Notice that these numbers are related to each other: They are all divisible by eight.

When an eight-tooth gear, intermeshed with a 24-tooth gear, rotates one complete turn, it will turn the 24-tooth gear one-third turn. That will cause a 3-to-1 reduction in speed, and gain in power.

If an eight-tooth gear intermeshes with a 16-tooth gear, every rotation of the eight-tooth gear will cause the 16-tooth gear to turn one-half time. That is a 2-to-1 decrease in speed and increase in power.

This is exactly the kind of thing happening on your mountain bike, except the gears are meshed by means of a chain.

That raises the interesting question about gear chains. What if you hooked up a series of gears in a row?

If you set up two 3-to-1 gears in a row, the final power decrease would be a 9-to-1 loss.

If you were to set up a 3-to-1 gear followed by a 5-to-1 gear, the decrease in speed would be 15-to-1.

There are other interesting numbers about Legos, though I’m not sure they are as important as the ones I’ve mentioned.

According to “The Ultimate Lego Book” (DK Publishing 1999), two eight-stud bricks can be combined in 24 different ways. Three eight-stud bricks can be combined in 1,060 ways. Six eight-stud bricks can be combined in 102,981,500 ways.

By the way, this book would be an inspiration to any budding Lego builder.

Perhaps the last number that is important to the Lego world is the 1932 Depression.

That’s when Kirk Christiansen in Denmark began making toy trucks to enhance his carpentry business because of the Great Depression.

He filled his trucks with little wooden bricks and found people returning to buy more bricks. Lego was born.

Maybe 1932 is my favorite number.

Gary McCallister is professor of biology at Mesa State College and also CEO of Flaming Moth Productions.


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