Drawing a non-euclidean triangle on the surface of a sphere

kpaesel shared this question 4 years ago
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Does anyone know how to draw a triangle on the surface of a sphere, to illustrate how the sum of the angles is greater than 180 degrees? Drawing a sphere is no problem, but I don't know how to draw the triangle.


Thanks, Keir

Best Answer
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Hi, something like that ?

Comments (8)

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Hi, something like that ?

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Hi Michel- Yes, that looks great. I'm trying to follow your construction protocol, but I don't know how to do line 5. (after you make the 3 points.) Would the command be circle or intersect? Thanks, Keir

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c is just the circle through A and B with center (0,0,0) created with the intersect of the plane (0,0,0)AB and the sphere a

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I have worked through your construction protocol and can mostly follow it. However, sometimes my unit vectors point the opposite direction that I want. I can fix it by switching around the points that define the plane used to create the circle, but then both vectors on that plane switch direction instead of just one. Any suggestions?


https://www.geogebra.org/o/Fe5Q3ZXc

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e.g. a test with the tangent vector (AB) and and vector(AB) with the scalar product to turn 180° or not

vAB = Vector[A, A + If[Vector[A, B] UnitVector[Tangent[A, c]] > 0, 1, -1] UnitVector[Tangent[A, c]]]

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Ok, great, I'm almost there:

https://www.geogebra.org/o/Fe5Q3ZXc


I've learned a lot!


How do I add the angles? Seems so basic, but I can't figure it out. Should I do this within the text tool or add them in the algebra section and then select the sum in the text tool. How do I type greek letters in the algebra section: \alpha does not seem to work


How do I change the font size and weight of labels, for example for the angles?


Thanks so much!

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Using the input bar :

Angle[<vector1>,<vector2>]

by default, the first angle will by named : alpha

You can also use : Alt+a or the view>keyboard or the table of character opened with the character at the end of the input bar.

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