Hyperbolic Geometry

Hyperbolic Shape
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[/img][br][br][img]https://cdn.britannica.com/79/1479-004-AFEEC05F/Hyperboloids-sheet-sheets.jpg[/img]
Investigate Triangles
List down the properties of a triangle that you have learned before.
Now construct a triangle using the hyperbolic applet below.[br]What do you notice?
Investigate Rectangles
List down the properties of a rectangle that you have learned before.
Construct a rectangle using the hyperbolic applet below.[br]What do you notice?
Lambert & Saccheri Quadrilaterals
In this world (hyperbolic space), rectangles cannot exist because[br][list=1][*]the surface "curves away" from the corners.[/*][*]a four-right-angled shape is a logical impossibility.[/*][/list][br]So, we call these shapes the Saccheri and Lambert quadrilaterals.[br]They are special shapes that try to be rectangles but end up with acute (sharp) angles.
Exploration
Try out using the Poincaré Disk Model applet below to[br]1. Form a quadrilateral with two equal sides perpendicular to a base. Observe all their angles.[br][br]• Draw points A and B to create a hyperbolic line on the Poincaré disk. [br]• Using the 'Hyperbolic Perpendicular Bisector' tool, construct the perpendicular bisector of segment AB at E.[br]• Using the 'Hyperbolic Perpendicular at Point' tool create two perpendicular lines to AB at point A and B respectively.[br]• Set another point F on the perpendicular bisector of AB.[br]• Using the 'Hyperbolic Perpendicular at Point' tool, create a line perpendicular to EF at F
Now try using the Poincaré Disk Model applet above to[br]1. Form a quadrilateral with three right angles. Observe the fourth angle.
Note:
A Saccheri quadrilateral has two equal sides perpendicular to a base.[br]The summit angles of a Saccheri quadrilateral are acute.[br][br][br]A Lambert quadrilateral has three right angles.[br]The fourth angle of a Lambert quadrilateral is acute.
Close

Information: Hyperbolic Geometry