On a recent trip to India, I was asked by my nephew and niece to suggest some idea for their science project. I suggested them to look for a book in our library that I used to read growing up and had lots of fun doing so. I distinctly remembered that it was a Russian publication and after some searching we found the book. I had a great time revisiting the old memories and the kids had fun trying the brain teasers. Here it is
Fun with Maths and Physics : Brain Teasers Tricks Illusions by Ya. I. Perelman (MIR Publishers Moscow)
Its always a great pleasure to see kids being amazed by science and maths.
I came back from my wonderful trip and I forgot all about it. A few days ago I was discussing with a friend of how mathematics gets complex for high school students and that too so quickly, that it may become challenging for them to grasp all concepts and formulas. That's when I recollected one very neat & unique way I understood a basic formula which we all know too well:
(a+b)2 = a2 + 2ab + b2
Now how does one explain this to a young impressionable student or friend? Why does it have to be this way only? Why not 3ab, 8ab, b3or a5. Here is a good visual example that can help explain the concept more clearly.
To find the answer to (a+b)2 = ?
1. Consider a line L. Lets say we divide the line into 2 non-equal parts, "a" and "b".
L = a + b
2. Lets construct a square with side length as L consisting of a and b.
The area of this square is L x L which in turn is (a+b) x (a+b) = (a+b)2
3. How can we simplify the problem? Lets divide the square visually into "a" and "b"as follows.
4. And now finally we will assign the values of the area four different quadrilaterals to get the value of (a+b)2 as shown below.
From the above we can say, (a+b)2 = a2+ab + ab + b2 = a2 + 2ab + b2 .
Now we don't have to remember what the formula is, because you now know how you got to it. Now we understand it and that I think is a phenomenal thing. Once we grasp a concept we are unlikely to forget and more likely to put it in use.
I hope this was entertaining. Till next time..ciao
Sushant
Thanks Sushant for the fun refresher of this basic math concept.
ReplyDelete"Mathemagics" is the most accurate depiction about (a+b)^2 that I can remember. It is accurate, not because it captures intellectual debate or politics, but because it knows two things: (1) math concepts come and go, and (2) knowledge lasts forever. This is Sush's best post in years, muted, gentle and interesting.
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