up to and including the maximum value of p. For this it is easiest to use the spreadsheet. You must now make p evenly spaced points on c. To make the angle a, inputĭrag A along c and change p and q to make sure your construction is correct. You can find the angle A makes with the positive \(x\)-axis by using the function atan2. Make a circle c with O as its centre and d as radius, then make a point A on c. Make a point O at the origin and a unit circle called unit. For what values of p and q is d undefined? If you change the values of p and q, d is shown as undefined in the algebra view for some cases. Make two sliders p and q taking integer values greater than or equal to three.Ĭonstruct the hyperbolic distance d by copying the formula. GeoGebra-construction of hyperbolic tiling with centred polygon You will also need the hyperbolic tools HypPerpendicularBisector and HypCompass described in GeoGebra constructions in the Poincaré disc: Exercise 3 and Exercise 7 Exercise 1 You can either make them yourself by following the instructions on GeoGebra constructions in the Poincaré disc or copy the activity Basic hyperbolic tools. When making the hyperbolic constructions you will need hyperbolic tools for making a: line, segment, ray, distance, and circle. Create a tool HypRotate that has hrotate as output object and B, α, A as input objects.Make a circumcircular arc through K_1, A, and K_2, call it hrotate.Rename the intersection points to K_1 and K_2. Make the intersection points between c and the unit circle: Intersect]. ![]() Make the circle c through C and A: c = Circle.Make the intersection C between b and a'.Make the perpendicular bisector b between A and A': b = PerpendicularBisector.Make the centre M of hline: M = Centre. ![]()
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