Shirali, Shailesh
(2018)
Extending the definitions of GCD and LCM to fractions.
At RIght Angles, 7 (2).
pp. 3338.
Abstract
Tt happens quite frequently in mathematics that we
need to extend the definition of a mathematical concept
to cover a larger domain than the one on which the
concept was originally defined. Historically, such a
progression is part of the very evolution of mathematics.
To give a simple example, consider the notion of sine and
cosine of an angle. These notions arise from the
consideration of rightangled triangles. If we stick strictly to the original definition, then it becomes absurd to talk of the sine and cosine of an obtuse angle. But one can easily extend the domains of definition of these functions to cover angles of arbitrary measure by considering, instead of a rightangled triangle, a circle of unit radius centred at the origin of a rectangular coordinate plane.
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