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Cinderella.2, the recent model of the well known interactive geometry software program, has turn into a fair extra flexible software than its predecessor. It now includes 3 attached components: An better geometry part with new beneficial properties like variations and dynamic fractals, a simulation laboratory to discover uncomplicated legislation of Newton mechanics, and a straightforward to exploit scripting language that allows any consumer to quick expand the software program even further.
The Cinderella.2 Manual is the 1st ebook to provide entire guide and strategies for utilizing Cinderella.2. It includes a wealth of examples, particularly for the CindyScript language which interacts easily with the geometry and simulation elements, and an entire reference. Cinderella.2 is Math in movement all of the method, and this ebook offers accomplished documentation from begin to finish.
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Extra info for The Cinderella.2 Manual: Working with The Interactive Geometry Software
For a readable introduction to projective geometry we refer to the books of H. S. M. Coxeter on that topic [4, 3]. 3 Homogeneous Coordinates On a computer we unfortunately do not have geometric objects as primitive data types. A point or a line has to be represented by numbers: the coordinates. Usually, a point in the plane is described by its (x, y) coordinates. A line may be given by the three parameters (a, b, c) of its deﬁning equation ax + by + c = 0. However, when we want to do projective geometry, this turns out to be impractical.
Usually, these problems are resolved by conditionally controlling the visibility behavior of geometric elements by intersection properties (socalled Boolean points). 2 also offers this functionality, but at the same time, CindyScript provides a much better and more elegant way of dealing with this problem. CindyScript is a full-featured high-level programming language in which it is easy to implement arbitrary algorithmic behavior. Thus even complicated algorithms can be included on a general level in a dynamic geometry environment.
It was observed by the Pythagoreans that there is no rational number measuring the length of a diagonal of a square with sides of length one. Through application of the Pythagorean theorem, this task is equivalent to ﬁnding a number x such that x2 = 2. This discovery led to a deep crisis in the foundations of ancient geometry. However, the story of extending the number system does not stop at that point. One of the extensions, with perhaps the most drastic consequences, was the introduction of complex numbers.