POINT LINE HYPERBOLIC

NEWS

2019/8/22
First release of PointLine Hyperbolic.

download

Windows
PointLineHyperbolic version 045 (2019/10/18, stable)
Mac OS
PointLineHyperbolic version 042 (2019/08/20, not stable)

document

About

PointLine hyperbolic is one of works of the Ahara laboratory, Meiji University. This software allows us to construct a figure of the hyperbolic planer geometry. After finishing the construction, users are allowed to move vertices by mouse-dragging and to observe the variation of the construction. These kinds of software are called interactive geometry software (IGS) and many of IGS for Euclidean geometry are known such as GeoGebra.

PointLine Hyperbolic is a geometry tool for the hyperbolic geometry and it allows us to draw hyperbolic lines and hyperbolic circles in the Poincare disk model. In almost all IGS, construction has a procedure, a sequence of constructive modules. That is, we have some tools to make a figure, for example, a ruler and a compass, and we use these tools in a fixed procedure or principle to complete the figure.

Here is an example. Let us consider making a large circle and three small circles inscribed in the large one. Usually, it is not easy to draw such figure, because we don't know the procedure of construction of the figure in usual senses. But in PointLine, we only draw four circles, and make demands "set each pair of circles are tangent to each other." Here we consider no dependency but a relation between each two circles. Indeed, after finishing the construction of this figure, we are allowed to move any of the circles on teh screen.

manual (under construction)

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exercise (under construction)

(The hyperbolic orthocenter of a hyperbolic triangle)
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(Newton's second theorem may hold?)
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(Four midpoints of a quadrilateral (is not a parallelogram.))
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(A right triangle with the center is not inscribed.)
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(The supremum radius of the inscribed circle of a triangle)
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(Pappus' theorem)
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(Pascal's theorem)
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(Newton's first theorem doesn't hold in the hyperbolic geometry)
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(Simson's theorem doesn't hold in the hyperbolic geometry.)
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FAQ

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link

PointLine
PointLine (for Euclidian geometry)
Author
AHARA's Homepage