building a windmill
The geogebra activity here https://www.geogebra.org/m/dP7BAuZy#material/NAgxehQb shows a spinning windmill. This page will show you how to create animations like this, step by step.
In the microworld below, scroll on the the left bar until you see "Point O".
Click on "Point O", "Point A", "Point B", and "Point C" and see what happens.
To make this geogebra, I created points A, B, C and then created triangle [ABC] using the polygon tool.
Then I renamed it "blade_shape". To see where this is, click on the left cell for blade_shape and see it hide and unhide.
The slider t shows angles in radians.
Then I used the tool "Rotate around point" to rotate "blade_shape" around point A by angle measure t. To do this, I did the following:
- clicked on the "rotate around point" tool
- clicked on the middle of the the triangle blade_shape
- clicked on the point A
- typed "t"
- go to the link https://www.geogebra.org/geometry/fgf8rupz
- scroll up the left bar until you see the slider t.
- open up the "settings" for the slider t (in the left bar, click on the three dots next to the slider)
- change the "repeat" option from "oscillating" to "increasing"
- Now try pressing "play" again and see the windmill keep rotating the same direction!
Windmills typically have more than one blade.
We can create more blades by using the "Rotate around point" tool. Here's what I did:
- clicked on the "rotate around point" tool
- clicked on the middle of the the triangle blade
- clicked on the point A
- typed "90°"
To keep creating more blades, I took each newly created blade and followed the same steps. For example:
- click on the "rotate around point" tool
- click on the middle of the the triangle blade'
- click on the point A
- type "90°".
How would you create an animation like this, but with 5 blades?
How would you create an animation like this, but with 5 blades and a non-isosceles triangle shaped blade?
In the windmill animation example at https://www.geogebra.org/m/dP7BAuZy#material/NAgxehQb they used a different technique. If you're interested, read on. Otherwise, if the above is good enough for you, you can stop here.
To follow along, open a copy of the below geogebra here: https://www.geogebra.org/geometry/mpgwzqz6
To create the above, I did the following:
- Create slider T from 0 to 2pi
- Define point A
- Define point B
- Use the tool "Circle with center" create a circle with center A going through B
- Use the tool "Angle with given size" to create an angle of measure T: click on tool, click on B, click on A, type "T". This creates point B' so that angle BAB' has directed angle measure T radians.
- Create a smaller circle around B'.
Next, go to the copy of this and:
- Create two points C and D, at each of the intersection points of the small circle and big circle.
- Create a polygon [ACD]
- Rotate [ACD] about A by 120°
- Rotate [A'C'D'] about A by 120°
If you click the play button for the slider for t, you will see the blade go back and forth if you wait long enough. But that's not what a windmill does! A windmill should keep going.
To see how this works,
- go to the link https://www.geogebra.org/geometry/fgf8rupz
- scroll up the left bar until you see the slider t.
- open up the "settings" for the slider t (in the left bar, click on the three dots next to the slider)
- change the "repeat" option from "oscillating" to "increasing"
- Now try pressing "play" again and see the windmill keep rotating the same direction!