I was reading this great book on Maths. 1089 and all that by David Acheson
Just 167 pages of a book the size of the palm of my hand
Some questions the author raised had me thinking
1. Why is Negatives times Negative = Positive ? What is the proof ? What is the application ?
2. What is the best way to place three circles fully inside a triangle, such that the circles occupy maximum area. We need to vary the radius of circles to maximize the area. Each circle can have different radius
3. How much area is required to turn a stick of length 'd', by 180 degrees. Assume you have to move in 2 dimensions (Hint it is less than area of circle)
4. Prove Pythagoras Theorem square(a) + square(b) =square(c)
5. Why is pi connected to the series 1 -1/3 +1/5 - 1/7 + 1/9 ..... . After all pi is related to area of circle, so what is connection !!
6. What exactly are complex numbers. If they are imaginary why do we need it here in the real world
7. Did you know the i (complex number) e (natural log base) and pi are related by Euler Formula !!
8. If there are 4 cities and we want to connect them with roads. Assume the cities are in four corners of a square. What is the best way to connect them with minimum road laying cost. (Hint: Answers is not Minimum Spanning Tree and neither is it 2 diagonals !!)
9. Why is the book called 1089
Read if if you get a chance, it is available in Christ Library
3 comments:
Negative times negative is positive because when we negate an action twice it negates itself and makes it opposite of negative!
Hope you found this yourself already! :)
Ans 3) Yes it is less than area of a circle, in fact it is half of the area of the circle with radius d/2.
[where d is the length of the stick].
Ans 8) perhaps, the cost effective way in connecting the cities should be finding the center point for all the cities and laying road from all the cities to that center point. And i think that would look like diagonals of the square! Not sure if there is a better way than that exists!?! :)
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