Drag the sliders to create different Christmas wreaths.

Irina Boyadzhiev, Dec.8, 2015, Created with GeoGebra

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Drag the sliders to create different Christmas wreaths.

Irina Boyadzhiev, Dec.8, 2015, Created with GeoGebra

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Labels:
Christmas-wreath,
dilation,
rotation

The applet demonstrates the following:

*An ellipse is the set of all points in the plane, the sum of whose distances to two fixed points (foci) remains constant. *

A string with the selected length is attached to both foci and is kept tight by the tip of the pencil.

Irina Boyadzhiev, April 19, 2015, Created with GeoGebra

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Irina Boyadzhiev's GeoGebra Applets

- Select the length of a piece of string by dragging the endpoints of the blue segment.
- Drag the
**orange**point to select the position of the focus F1 along**the x-Axis or the y-Axis**. The other focus F2 is symmetrical to F1 with respect to the origin.

A string with the selected length is attached to both foci and is kept tight by the tip of the pencil.

- Drag the tip of the pencil or press the “Draw” button to trace all points on the plane that satisfy the above definition.
- Hide the pencil by pressing the "Pencil ON/OFF" button; show the ellipse by pressing “Show Ellipse” button, and explore the curve by changing the positions of the foci and the length of the constructing string.
- Bring the two foci to the origin to see the circle as a special case of the ellipse.
- Click on “Labels” to see some terminology.

Irina Boyadzhiev, April 19, 2015, Created with GeoGebra

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Irina Boyadzhiev's GeoGebra Applets

Labels:
conics sections,
ellipse

This applet demonstrates the correspondence between the points on the number line and the points on the unit circle.

Irina Boyadzhiev, January 9, 2015, Created with GeoGebra

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Irina Boyadzhiev's GeoGebra Applets

- Enter a real number in the “step” input box. Try the applet with whole numbers, fractions, multiples or fractions of pi. (Example: pi/4)
- Select “Wrap Positive Numbers” or “Wrap Negative Numbers”.

** Notice**, you have to deselect one checkbox in order to be able to select the other one.

Irina Boyadzhiev, January 9, 2015, Created with GeoGebra

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Irina Boyadzhiev's GeoGebra Applets

Labels:
number line,
radian measure,
unit circle

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