No Fear For Mathematics - Duality

Описание: https://www.cheenta.com/no-fear-for-m...

No-fear-mathematics is a new course at Cheenta. This is for children and adults who want two things:

1. fall in love in mathematics and see how beautiful it is
2. build a strong foundation in mathematics so that they can solve problems

So, how do we do this?

How do we remove fear from the mind of students who have learnt to be afraid of mathematics in our school and society? This is especially true in India but it is also true in other places of the world. Children think of mathematics as this ruthless, dry subject, where you learn a bunch of formulae and plug them into problems.

We have designed this course in a completely different way. We want our kids to fall in love with the subject. We have tried these methods for over a decade now. We think we have learnt how to help kids enjoy mathematics rather than be afraid of it.

The No-Fear-Mathematics program is through live classes and mathematics laboratory sessions. You can check it out in the link the description.

Our mission is simple: remove fear and share how beautiful mathematics is.

In this video and in the upcoming ones, we will share with you, some of the methods that we are using in this NO-FEAR-MATHEMATICS COURSE.

Today let us talk about one such method: Engage with mathematical patterns by doing

In this session we will learn about DUALITY in mathematics. Duality is actually a philosophical idea. In Vedantic tradition of Indian Philosophy we have the dual notion of Purush and the Prakriti. In Chinese philosophy, there is a notion of Yin and Yang. You should definitely look up the philosophical aspects of DUALITY online.

We will discuss a mathematical aspect of this concept.

Lets start by drawing a cube. We will mark the midpoints of each of the faces of this cube. How many faces are there? 6 of them right. So we will have 6 midpoints.

We will connect pairs of these 6 midpoints using a rule. Connect two points if they are midpoints of faces that share an edge. This is known as the adjacency relation. Lets make this a little bit more clear.

The top face is HGFE. It is attached to the face FEAB along the edge FE. So we join the midpoints I and M using a segment.

Now, it is your job, to tell me, what happens, if you join all such segments. What kind of shape do you get? Can you draw it?

Use the software GeoGebra to actually make this model and experiment with it. Experimentation is very important to learn mathematics.

Finally whatever shape you get inside the cube, repeat the same process again. That is mark the midpoints of the faces of that shape and connect them with segments if they are adjacent. What shape do you get then?

Can you explain why this phenomenon can be regarded as duality?