Why the sum of exterior angles of any n-sided polygon is 360 °? 1. Firstly, let’s take any n-sided polygon and construct their exterior angles taken either clockwise or anti-clockwise as shown in the given figure. 2. In the given figure, a, b, c, d, e,… are the interior angles and a’, b’, c’, d’, e’,… are the exterior angles of n-sided polygon ABCDE. 3. We know, the no. of exterior angles formed will be equal to the no. Of sides of polygon (n). 4. By the rule of straight angles, we have: a + a’ = 180 ° , b + b’ = 180 ° c + c’ = 180 ° , d + d’ = 180 ° , e + e’ = 180 ° and so on.. Here, adding them all, we get: (a + a’) + (b + b’) + (c + c’) + (d + d’) + (e + e’) +… = n*180 ° [ there are n straight angles when the sides are extende...
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Margaret Hamilton The Woman Behind the First Manned “Journey to the Moon” Background “We choose to go to the Moon''. These words by the then US president John F. Kennedy, addressing the crowd of prestigious Rice University in 1962, was no sort of relief for Americans who feared the overwhelming Soviet Union and the US falling short in what was to be ‘first’ to land man on the moon. Soon after, the courageous and ambitious ‘Journey to the moon’ had its first dedicated mission ‘The Apollo Program’ which despite initially being destined for a trip to Mercury shifted its ambitions a little close to the earth, the lunar surface. The Apollo program, by NASA, was successful in landing the first Manned spacecraft on the Lunar surface just 7 years after its rejuvenation under President John F. Kennedy. The first Lunar module landed the likes of Neil Armstrong, Micheal Collins, and Edwin Aldrin but little do they know the mind behind the software that orchestrated the mo...
Why is any number over 0 undefined or what we say infinity? We are used to dividing a certain number by another or by the same number since we started learning mathematics. That’s not a big deal. But here’s one big deal that we are always warned about i.e., to divide any number by zero (0). But Why? Because you get infinity when you do so. But how and why we tend to get so when we divide any number by zero? Let’s have a look at it to better understand!!! ▪ Firstly, what’s multiplication? Nothing but repeated addition. Example: 2×3=6 which means we need to add 2 thrice to get 6. ▪ And secondly , what’s division? Nothing but repeated subtraction unless we get zero. Example: 15/5=3 which means subtracting 5 thrice from 15 to get 0. i.e, 15-5-5-5=0 But let’s check in case of 1/0. Accordin...
Imagine, it’s a life or death question. And you don’t even have a calculator. How do you even make sense of the given question? But mathematics has this way of surprising us, and often, it surprises us with connections we’d have never imagined. In this article, I’ll present to you two methods that you can use such connections to easily get to the answer to the above question. 1. Taylor comes to rescue! Ever herad of Taylor expansion? Well, it’s nothing more than approximating non-polynomial functions using polynomials. Yes, all the sine, cosine, log, and exponential functions have a Taylor approximation of their own. More on that later! I think, not necessarily knowing the name for the expansion, everyone would be well aware of the expansion of e^x, the exponential function. You can even derive the expansion easily using the definition of e and binomial expansion. Why don’t you try it on your own before having a peek at the expansion below? Now, as you can see, the exp...
What's 2 × 2 ? It's 4. What's 3 × 3 ? It's 9 What's 4 × 4 ? It's 16 What's 2 . 5 × 2 . 5 ? It's 6.25 What's 2 √ × 2 √ ? It's 2 What's − 4 × − 4 ? It's 16 And so on You can clearly observe that for a certain number, the result obtained by multiplying that certain number with itself is a l w a y s greater than that certain number. Is it really though? No, it's not always. Here let me give you an example, What's 0 . 5 × 0 . 5 ? It's 0 . 25 Looking at it graphically, Below is the graph for f ( x ) = x 2 In the interval ( 0 , 1 ) we can see that the f ( x ) i s l e s s t h a n x . So clearly the result obtained by multiplying that certain number with itself is 𝑛𝑜𝑡 a l w a y s greater than that certain n...