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Unit-1 Why Learn Mathematics

This unit discusses what mathematics is, its characteristics, processes involved in developing its ideas and hierarchy of its ideas.

Several circles can be drawn through a point. How many can be drawn through two points, or three points, or.…?

i)Work on this problem and note down the processes you use.

ii)Did the properties of mathematics, mentioned in Sec.1.3, show up while you were developing your arguments? If so, in what way?





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Learning Pundits Content Team

Written on Apr 17, 2019 6:29:05 PM

•As there can be made infinite lines from a given length. Let us consider those lines as the diameter of the circle, then we get infinite number of circles.

•Now, the line between the 2 points will be a chord of the circle and if we perpendicularly bisect the chord, we can have infinite number of circles by considering center on the bisector with diameter as the distance between center to one of the point.

•Lets consider there can be infinite circles through 3 points. This will be true if the points lie on the same line. But otherwise, there can only be 1 unique circle. It can be proved using properties of chords and circle.

i)So, in all the cases, we first propose a conjecture. If it proves to be true, fine. Otherwise, we propose another conjecture and try to prove or disprove it.

ii)The properties mentioned are used in our steps for reasoning mathematically.

 Conjecture -> prove/disprove -> new conjecture (if required)