Triangles to Tetrahedrons and beyond…

Azim Premji University, Math Space (2020) Triangles to Tetrahedrons and beyond…. At Right Angles (7). pp. 58-66. ISSN 2582-1873

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The seed-idea of this article came from an activity from an upper primary math textbook and the modification in a subsequent edition. Students were asked to find the midpoints of the sides of an acute isosceles triangle and join them to form four smaller triangles, and then fold the triangles up to a tetrahedron. An equilateral triangle replaced the isosceles one in the subsequent edition. What caused this change? Wouldn’t any triangle generate a tetrahedron? This initial exploration revealed something unexpected and the findings had an eerie resemblance to a known result. Further discussions with more math-friendly minds watered and added subsequent layers to this exploration and took it to a newer dimension – figuratively and literally! If a perpendicular is dropped from the apex (which is the top vertex of the tetrahedron where all three vertices of the triangle meet) to the base, where will the foot of this perpendicular be? For an equilateral triangle, it is the centre of the base but would it ever be coincident with any of the triangle centres, i.e., centroid, circumcentre, incentre or orthocentre of the base for other triangles? We will investigate these.

Item Type: Articles in APF Magazines
Authors: Azim Premji University, Math Space
Document Language:
Uncontrolled Keywords: Triangle, Tetrahedron, Constraint
Subjects: Natural Sciences > Mathematics
Divisions: Azim Premji University > University Publications > At Right Angles
Full Text Status: Public
Publisher URL:

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