Sunday, April 19, 2015

On the Geometric Definition of Ellipse

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. 

  • 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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Saturday, January 10, 2015

Radians, Number Line and the Unit Circle

This applet demonstrates the correspondence between the points on the number line and the points on the unit circle.
  • 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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Thursday, April 17, 2014

Applet on Counting the Number of Squares in a Chessboard

This applet models how to count the number of squares in the chessboard.

Monday, February 10, 2014

Midsegmens and Congruent Triangles

A midsegment of a triangle is a segment that connects the midpoints of any two sides of the triangle. This applet demonstrates that the three midsegments of any triangle divide the original triangle in four congruent triangles. The demonstration is based on the following properties:
  1. The midsegment is parallel to the third side of the triangle. 
  2. Any parallelogram has a rotational symmetry with center the intersection point of the diagonals and angle of rotation 180∘

Irina Boyadzhiev, 9 February 2014, Created with GeoGebra

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