This Demonstration illustrates the concept of rotating a 2D polygon. The rotation matrix is displayed for the current angle. The default polygon is a square that you can modify.
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In physics and mathematics, series expansions to approximate functions are often used because using the exact solution is either impossible or involves unnecessary complicated calculations. This Demonstration shows accuracy for a series of expansions and how adding terms increases that accuracy moving away from the origin.
If two inscribed angles intercept the same arc, then the angles are equal. Drag the orange points to change the figure.
A dynamically simplified solar system is constructed from online data to explore the real solar system on many different scales.
The realistically scaled solar system is surprising because nothing is visible due to the presence of many different scales. That is why it is usually rescaled in animations or illustrations. This is nice but gives us a wrong sense of distances and sizes. This Demonstration is intended to show the solar system's different scales in their full glory.
Since it is hardly possible to see anything when the real scales are used, controls have been added to modify the sizes of the celestial bodies.
This Demonstration shows 3D bar charts of the periodic table with various element property values.
Improve your ear by learning to recognize pitches in the context of a key. Use the radio buttons to decide if you want to practice in a major or a minor key, whether you want to use notes only from the tonality you chose or from all twelve notes of the chromatic scale, and whether you want to hear the scale or a cadence in that key as a reference. Choose the range (in number of octaves) from which you would like the note selected. Click the "new example" button and the scale or cadence will be played, followed by a note selected at random subject to your restrictions. It is up to you to determine the note that was played. If you need to hear the randomly selected note again, click the "repeat note" button. You can check your answer by ear or you can have the answer displayed for you by clicking the "show answer" checkbox. The "fixed tonic C" checkbox lets you always work in C major or to have the tonic selected at random with each new example.
Algebra students need practice determining equations of lines given a pair of points, or the line parallel or perpendicular to a given line through a given point. This Demonstration, along with guiding worksheets or a teacher presentation, gives students a chance to see the relationships between these lines and points.