Title: A friendly local community for diversity-From the experience of living abroad- 19 November 2021 Saku-Sozokan,

Faculty of Saku, Nagano Senior University

The IMI Education Department has launched IMI Math class in which we provide a series of videos on Precalculus (School Mathematics).

We also launched "Dr Ken's Calculus" too.

Achilles and the Tortoise

Achilles is in a footrace with a tortoise. The tortoise is given a head start at a certain distance.

Then they start at the same time. When Achilles reaches the tortoise's starting point, the tortoise has moved forward. Then Achilles reached the position of the tortoise but the tortoise has already moved forward and so on. This continues forever. Therefore, Achilles cannot catch up with the tortoise.

Is this true?     

This is one of Zeno's paradoxes. This statement claims that Achilles cannot catch up with the tortoise until he catches up with the tortoise. This means that if there exists the exact point in which Achilles catches up with the tortoise, then he can catch up. We assume that there is no such a hole on the real line, so on the real line, Achilles can catch up with the tortoise. Thus this paradox relates to the concept of continuity of the real line.

Knotted?

A knot is a knotted circular string in the space. Knot Theory studies if a tangled circular string is really knotted. Is the following string knotted?

Every knot diagram can be deformed into another diagram by a finite sequence of small modifications. This diagram can be deformed into a trivial circle. Therefore, this is not knotted.

Lectures