Indigenous aspect of thinking

I was struck by the connection between the geometry and the clothing. I was amazed to realize that that linearity corresponds to the tension in the fiber. Therefore, the math is everywhere, it just requires our awareness and keen observation. It is important to notice how beautifully the grid is used as a metaphor to describe the control and ownership. My second stop was at anything that is real is independent of the grid system. As no grid system can explain the underlying geometry of the shape. Hence I really liked the idea of shifting the focus to understanding the geometry rather than focussing on using the grid system according to our convenience.

The idea of starting off with the simpler knots and then extending to the 3-D knots gives the students an opportunity to go beyond the rectilinear thought and also open their minds towards how the indigenous people get connected with their culture and looking for the mathematics behind the different geometries.

Math fair by MacNair Secondary students

The  Math fair by the MacNair Secondary  School students was amazing. There were such new ideas of representing the things I never thought, such as representing the integers ( their multiplication, division of negative, positive numbers) in the fun and interesting ways like " Did the turtle eat the cookie". I was really impressed by their ideas. I believe that students have a lot of potentials, emerging thoughts, and innovative ideas and they look at things through a different lens which is more meaningful to them. In addition to this, It was pleasing to see how the stories they made led them to solve the linear equations and made more sense to them which was much more effective than simplifying solving for the variable. " Fire and the water metaphors for positive and negative integers were interesting to see. I wish the best for those students and their teacher who is successful to build the student's faith in him. I wish for their success and hope that they would make a difference in the traditional ways of thinking about math and My big thanks to them and to their teacher for imparting new ideas to me and to my fellow mates.

Rat and wine puzzel

I will start with the small number of bootles and rats and then extend.
Let's consider rat 1 and only 2 bottles out of which one of them contains poison.
If the rat 1 drinks bottle 1 and die then bottle 1 contains the poison, but if not them the bottle 2 contains the poison.
Therefore 1 rat is required to test 2 bottles.
If we have 2 rats, then let's figure out how many bottles can be checked.
Rat 1 is given a mixture of 1 and 2
Rat 2 is given a mixture of 2 and 3
If rat 1 and 2 die then the bottle 2 is poisoned.
If rat 1 dies and rat 2 survives then bottle 1 is poisoned.
If rat 1 survives and rat 2 dies then the bottle 2 is poisoned.
If both the rats survive then the bottle 4 is poisoned.
Therefore, with 2 rats I am able to check 4 bottles.

Now let's start with 3 rats.
Rat 1 is given a mixture of 1,2,3,4
Rat 2 is given a mixture of 3,4,5,6
Rat 3 is given a mixture of 1,3,5,7

If rat 1 dies, number 2 contains the poison
If  rat 2 dies, number 6 contains the poison
If rat 3 dies, the number  7 contains the poison
If  all the 3 rats die, then number 3 contains poison
If  only 1 and 2 die the number 4 contains poison
If none dies number 8 contains the poison

Hence till now with 3 rats, I can check 8 bottles.
I can notice the pattern,
If there is 1 rat then the number of bottles check is 2
If there are 2 rats then the number of the bottles checked is 4
If there are 3 rats then the number of the bottles checked is 8

Therefore 2^n( 2 to the power n) where n is the number of rats.
hence 10 rats are enough to check 1000 bottles as 2^10= 1024
but for 9 rats I am not able to figure out as only 512( 2^9) bottles can be checked.