Azim Premji University, Math Space
(2020)
Triangles to Tetrahedrons
and beyond….
At Right Angles (7).
pp. 5866.
ISSN 25821873
Abstract
The seedidea 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 mathfriendly
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.
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