Published: March 29, 2017

Yes, there are equations on the rocks.

You might like them, you might want to run away.

You might wonder,

"Hey, there are LITTLE CHILDREN playing here, what are those equations doing here?"

or

"What should I say if my kids ask me about them?"

 

The quadratic equation etched on a rock3 large rocksThe equation x = (1+ squarer of 5) / 2 etched in stone

Pretend the rocks are like a fire station.  We take little kids to see the firefighters and trucks and dials and pumps and gauges without worrying if they understand it.

children at a fire station

Think about these rocks like a trip to a mathematical fire station.

The equations are cool looking. 

To mathematicians they are useful, just like pumps and fire trucks are to firefighters.

You can tell and ask your kids:

  • These equations describe patterns.
  • Patterns and equations tell storys, when you understand the math, you will understand the story.
  • You will see these patterns when you take Algebra in middle school or high school.
  • Ask which on they like best?  Why?
  • Do you recognize some of the numbers?  Do you know what some of the sympbols mean?
  • For fun, take super close up pictures.

abstract close up of an equation

  • Make up really crazy stories about what the equations mean. Are they for a trip to the moon? a treasure hunt? a formula to make gold?

a rocketship on the moonpot of goldold books, a crystal and a candle - an alchemy workshop

                 Harry Potter alchemy lesson

 

*The following is TOTALLY OPTIONAL*

These equations actually tell the story of the Golden Ratio 

This one tells us about the relationship of 2 rectangles, one inside the other.

A rectangle divided by the Golden Ratio - Long side x, short side 1, and short side of the interior rectangle is 1 - x.

(this image is from a great website, for more details - Derive Golden Ratio Page )

  • The rectangle inside has the same ratio as the orignal rectangle, and the short side is length 1.
  • x is the length of the long side, the thing we want to find.

The equation x/1 = 1/(x -1) etched in stone

  • So the left side says that (length of the long side) is the same proportion as 1 (length of the long side of the small rectangle)
  • And the right side says that 1, the length of the short side, is proportional to (x -1), the short side of the small rectangle.
  • Now we solve for x.
  • a little algebra and,
  • x2 - x - 1 = 0 

Now we need the quadratic formula to solve:

The quadratic equation etched on a rock

This is an important formula to know in algebra

Using it we find that x equals:

The equation x = (1+ squarer of 5) / 2 etched in stone

 

 

 

If you plug this into a calculator, you'll get:

1.61803399...

Which is the Golden Ratio

BUT WAIT THERE'S MORE!!!

Try dividing Fibonacci Numbers (the ones on the sides of the rocks)

2/1 = 2

3/2 = 1.5

5/3 = 1.666...

8/5 = 1.6

13/8 = 1.625

21/13 = 1.6153862...

34/21 = 1.6190476...

and so on.  Crazy right?

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