Web Scrapping

Math: Pascal Triangle unknown facts and mysteries

This may look like a neatly arranged stack of numbers, but it's actually a mathematical treasure trove. Indian mathematicians called it the Staircase of Mount Meru. In Iran, it's the Khayyam Triangle. And in China, it's Yang Hui's Triangle. To much of the Western world, it's known as Pascal's Triangle after French mathematician Blaise Pascal, which seems a bit unfair since he was clearly late to the party, but he still had a lot to contribute. So what is it about this that has so intrigued mathematicians the world over? In short, it's full of patterns and secrets. 

First and foremost, there's the pattern that generates it. Start with one and imagine invisible zeros on either side of it. Add them together in pairs, and you'll generate the next row. Now, do that again and again. Keep going and you'll wind up with something like this, though really Pascal's Triangle goes on infinitely. Now, each row corresponds to what's called the coefficients of a binomial expansion of the form (x+y)^n, where n is the number of the row, and we start counting from zero. So if you make n=2 and expand it, you get (x^2) + 2xy + (y^2). The coefficients, or numbers in front of the variables, are the same as the numbers in that row of Pascal's Triangle. You'll see the same thing with n=3, which expands to this. So the triangle is a quick and easy way to look up all of these coefficients. But there's much more. For example, add up the numbers in each row, and you'll get successive powers of two. Or in a given row, treat each number as part of a decimal expansion. In other words, row two is (1x1) + (2x10) + (1x100). You get 121, which is 11^2. And take a look at what happens when you do the same thing to row six. It adds up to 1,771,561, which is 11^6, and so on. There are also geometric applications. Look at the diagonals. The first two aren't very interesting: all ones, and then the positive integers, also known as natural numbers. But the numbers in the next diagonal are called the triangular numbers because if you take that many dots, you can stack them into equilateral triangles. The next diagonal has the tetrahedral numbers because similarly, you can stack that many spheres into tetrahedra. Or how about this: shade in all of the odd numbers. It doesn't look like much when the triangle's small, but if you add thousands of rows, you get a fractal known as Sierpinski's Triangle. This triangle isn't just a mathematical work of art. It's also quite useful, especially when it comes to probability and calculations in the domain of combinatorics. 

Say you want to have five children, and would like to know the probability of having your dream family of three girls and two boys. In the binomial expansion, that corresponds to girl plus boy to the fifth power. So we look at the row five, where the first number corresponds to five girls, and the last corresponds to five boys. The third number is what we're looking for. Ten out of the sum of all the possibilities in the row. so 10/32, or 31.25%. Or, if you're randomly picking a five-player basketball team out of a group of twelve friends, how many possible groups of five are there? 

In combinatoric terms, this problem would be phrased as twelve choose five, and could be calculated with this formula, or you could just look at the sixth element of row twelve on the triangle and get your answer. The patterns in Pascal's Triangle are a testament to the elegantly interwoven fabric of mathematics. And it's still revealing fresh secrets to this day. For example, mathematicians recently discovered a way to expand it to these kinds of polynomials. What might we find next? Well, that's up to you.

Geogera: Algorithm Bezier Curve Steps

Bezier Curve
1 Point A
2 Point B
3 Segment a Segment [A, B]
4 Point C
5 Segment b Segment [A, C]
6 Number n
7 List listAB Sequence[A + i / n (B - A), i, 1, n]
8 List listAC Sequence[A + i / n (C - A), i, 1, n]
9 List list3 Sequence[Segment[Element[listAB, i], Element[listAC, n - i]], i, 1, n]
10 List listBC Sequence[C + i / n (B - C), i, 1, n]
11 List list5 Sequence[Segment[Element[listAB, i], Element[listBC, n - i]], i, 1, n]
12 Segment c Segment [C, B]
13 List listCB Sequence[B + i / n (C - B), i, 1, n]
14 List list6 Sequence[Segment[Element[listAC, i], Element[listCB, n - i]], i, 1, n]

Geogebra: Divide Cirlce with n parts with polar view

https://www.geogebra.org/graphing/qz9nvmbp

Divide Circle with n parts

 Sequence(Rotate(B, i°, A), i, 0, 360, 360 / n)

Join segments from Center A to n points on circle circumference

 Sequence(Segment(A, l1(n)), n, 0, 100)

Coding Standards, Guidelines and Best Practices: Avoid Aysnc Void

Getting Started with Asynchronous Programming in .NET

by Filip Ekberg

Avoid Async Void

Use Async Void

Async Void is only appropriate for Event Handler

protected async void search_click( object sender, RouteEventArgs e)
{
     await GetStocks()
} 

Alternate Solution 

private async Task GetStock()

{

}

Take Away:
Async Void crashes an application or may results in 500 exception if something went wrong. As there is no way to propagate exception even you have proper try catch. 

Call GetStock()

private async void GetStock()
{
 try
{}
catch()
}

Geogebra: Circle with Sequence, Dilate and Segment geometry tricks

Learn Geometry 

You can open my geogebra activity and can try similar activity.

Click here

Draw Geometric Equilateral Triangle Crossed In Straight Line

Hint:

Sequence(Dilate(C, i / s, B), i, 1, s)

To divide segment into equal parts with dynamic points in it

Sequence(Segment(G, l5(n)), n, 0, s)

To create dynamic segments 

It makes lot of sense when you.....

It makes lot of sense when you're SEEN, HEARD and VALUED! If that is the case then you're actually part of it or you're acknowledged or you've been respected Otherwise that is not the place you should be.

Just imagine you're in a meeting or discussion, you're seen but not heard if heard not valued that means you're not required.

Now in this case you're part of the team and you're seen but heard perhaps not valued . Your opinion doesn't stands any good. In and all it is very important you should be seen , heard and at the same time valued. That means you're respected and people needs you.

So bottom line is, the only way you should feel you're R equired or C onnected or R espected, it is only through these sense of acknowledgment of being Seen, heard and valued .

Eventually it shapes your whole career path for Being what you're, Belong to place you want to be and Become is the path to your career progression ...you want to be.

If none of these happens then it is a call for ....?

Coding Standards, Guidelines and Best Practices: Group Enum and Constants