# Fashion Fridays: Rotations

November 16, 2018

Which of these was made to twirl? The hula hoop OR this gorgeous green floral ruffle dress from Free People? That’s easy- BOTH. Next question: What type of transformation would we need to use to make both our hula hoop and our runway model spin like a top? You guessed it… ROTATION.  This rotation helps the hula hoop become magical, mathematical, and perfectly complement creative thinking. Allow me to explain…

The hula hoop is spinning, or to put it another way, rotation is occurring.

Rotation is a type of shape transformation or change in appearance. When a shape rotates, it moves around a fixed center point either clockwise or counter-clockwise. The shape remains the same, but its position within the space changes. Rotation is measured in degrees from 0 to 360. We use a positive or negative number to show whether the rotation is clockwise (negative rotation) or counter-clockwise (positive rotation)

What does this have to do with fashion, you ask?  Well, take our math teacher on the runway, for example. We could ask her to turn to her left…

“Now turn to the left”

“What? Left?”

“Right… No, I mean correct.”

Or…

“Could you please rotate 270 degrees Dr. Jones?”

“…Sure… positive degrees means counter-clockwise… ?”

Aside from fashion, there are countless examples of rotation happening all around you, whether you realize it or not.

Just as in fashion, there will always be knock-off versions of the real thing. Can you “mathfashionistas” spot the fake? Which of these two rides should genuinely be labeled “The Rotation Express” and which one is just not quite authentic?

Did you spot the fake? Its the Ferris Wheel! While both of these rides show some characteristics of rotation:

• Circular motion on a coordinate plane

• Equal distance from the center point (origin)

• Doesn’t resize

• Doesn’t reflect

The carousel has those little details (like a great dress) that the Ferris wheel just forgot:

• Entire figure rotates simultaneously

• Orientation of the figure changes as it moves around the axis

If the Ferris wheel was a “genuine” example of rotational geometry, then the cars would be stuck in place, unable to move, and the unlucky passengers would be hanging upside down at the top! (can’t do that in a designer dress!) While the Ferris Wheel’s cars are all following a circular path around the origin, (the center of the wheel) the cars maintain their orientation throughout. No one is dangling upside down or sideways.

In contrast, picture the carousel from a drone’s camera hovering just above. Looking down at the carousel rotating, each horse stays stuck on its pole, so the rider moves with the whole carousel, facing lots of different views during their trip around the circle. The horses do not get to stare at the popcorn cart all the way around the circle. Their orientation changes as they rotate.

Just remember, in geometry, rotation simply means… SPINNING AROUND A POINT.

Another example of rotation is the agitation of a washing machine, sometimes it moves in a short, jerking motion others it’s spinning clock-wise or counter clockwise, but it’s never changing shape and it’s never changing distance from the center point. (Is it a real example or a fake?)

Rotation is near and dear to your heart, in fact, it’s near and dear to everyone’s heart! The opening and closing of your heart valves to control blood flow is another example of rotation. (Is it a real example or a fake?)

Now that you know rotation is a matter of life and death 😍 try to come up with some real-world examples of your own.

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