john212/pascals_triangle_r0a.html

## pascals_triangle_r0a.html
<!doctype html>
<html>
<head>
    <meta charset="UTF-8">
    <title>Pascal's Triangle Coefficient Calculator</title>
</head>
<body>

<h2>Pascal's Triangle Coefficient Calculator</h2>

<P>This program will calculate the coefficients of Pascal's Triangle up to
any row "r" specified by the user. The formula used is from the Binomial Theorem
where the coefficients of each term of the expansion of the binomial
(x + y)<sup>n</sup> are given by <sub>n</sub>C<sub>r</sub> read "a (C)ombination of
"n" things taken "r" at a time". The formula for <sub>n</sub>C<sub>r</sub> is n!/(n-r)!r!
where "!" is the factorial symbol. Note that since "r' is indexed at zero,
that is, the first row means r = 0, that means n, the exponent of the
binomial expansion, will be n, but there will be n + 1 terms and
therefore n +1 coefficients of Pascal's Triangle.</P>

<p>Factorial n written n! means (n)(n-1)(n-2)...(1)</p>

<p>By definition 0! = 1.</p>

<P>For example, row 3 of Pascals Triangle means n=3 (third row
of Pascals Triangle starting at 0) and r = 3; n is fixed but r
will run from 0 to n, i,e, 0, 1, 2, and 3 in this example,
so the coefficients of Pascal's Triangle are:</P>

<ul>
<li>3Cr = 3!/(3-r)!r! </li>
<li>3C0 = 3!/(3-0)!0! = 6/6*1 = 1</li>
<li>3C1 = 3!/(3-1)!1! = 6/2*1 = 3</li>
<li>3C2 = 3!/(3-2)!2! = 6/1*2 = 3</li>
<li>3C3 = 3!/(3-3)!3! = 6/1*6 = 1</li>
</ul>

<P>This program is written in JavaScript.</P>

<P>By Mr. C. January, 2020</P>

<P>*********************results********************************</P>

<script>

main();         //must call the main() function to run the program.
function main() //Envelope program in main() function
{ //start main() function block

var ptrows = "";          // Pascal's Triangle rows, indexed at 0.

// ask user to input the number of rowa
ptrows = prompt("Enter rows of Pascals Triangle", "Type the value here");
ptrows = parseInt(ptrows,10); //convert text input (string input) to an integer

// Data Validation - Ensure user input is >= 0 for r.
if(!(ptrows >= 0))
  {//start data validation if block
  document.write("<P>ptrows=", ptrows);
  document.write("<P>ptrows must be greater than or equal to zero");
  return; // stops execution of if block
  }//endof data validation if block

document.write("<P><b>Pascals Triangle Coefficients</b></P>");
document.write("<P>Number of Terms=", ptrows+1);
document.write("<P>N= ", ptrows);

// calculate the coefficients of each term
for(let i = 0; i <= ptrows; i++)
{ // start pt coefficient for loop
var ptcoefficient = 0;
ptcoefficient = nCr(ptrows,i);
document.write("<P>r = ", i, " coefficient ", ptcoefficient );
} // endof pt coefficient for loop

}//endof main() function block

// *****************************************************************************
// function to return the factorial of any passed integer
// note: the set of integers is abbreviated "Z"
function factorial(_Z)  // Z is set of integers, _Z means variable is an argument
{ //start factorial function block
  var counter = _Z; // will use the integer argument as the starting value of a counter
  var factorialZ = 1;
  if(_Z === 0)
    {//start if _Z is 0 if block
	factorialZ = 1;
	return factorialZ;
    }//endof if _Z is 0 if block
  while (counter >= 1)
    {//start while block
    factorialZ = counter*factorialZ;
    counter = counter - 1;
    }//endof while block
  return factorialZ;
} //endof factorial function block
// *****************************************************************************

// *****************************************************************************
// function nCr to return the combination of n things taken r at a time
function nCr(_n, _r)
{ //start nCr function block
var nMinusr = 0;
var combinations = 0;
nMinusr = _n - _r;
combinations = factorial(_n)/((factorial(nMinusr))*factorial(_r));
return combinations;
} //endof nCr function block
// *****************************************************************************

// *****************************************************************************
// function nPr to return the permutation of n things taken r at a time
// TBD-use nCr for model
// *****************************************************************************

// *****************************************************************************
// Console log variables for debugging - comment in/out as needed
/*
TBD
*/
// *****************************************************************************

</script>

<p><b>To check your answers, visit one of these sites:</b>
  <ul>
    <li><a href="http://mathforum.org/dr.cgi/pascal.cgi">Interactive Pascal's Triangle at MathForum.org</a></li>
    <li><a href="https://www.symbolab.com/solver/step-by-step/%5Cleft(x%2By%5Cright)%5E%7B5%7D">Binomial Expansion at Symbolab</a></li>
    <li><a href="http://ed.ted.com/lessons/the-mathematical-secrets-of-pascal-s-triangle-wajdi-mohamed-ratemi">Pascal's Triangle - Wajdi Mohamed Ratemi - TED Video</a></li>
    <li><a href="https://www.mathsisfun.com/algebra/binomial-theorem.html">The Binomial Theorem at MathIsFun.com</a><br><i>(check out the derivation of "Euler's Number" , aka "e".)</i></li>
  </ul>
</p>

</body>
</html>
	<!doctype html>
	<html>
	<head>
	<meta charset="UTF-8">
	<title>Pascal's Triangle Coefficient Calculator</title>
	</head>
	<body>

	<h2>Pascal's Triangle Coefficient Calculator</h2>

	<P>This program will calculate the coefficients of Pascal's Triangle up to
	any row "r" specified by the user. The formula used is from the Binomial Theorem
	where the coefficients of each term of the expansion of the binomial
	(x + y)<sup>n</sup> are given by <sub>n</sub>C<sub>r</sub> read "a (C)ombination of
	"n" things taken "r" at a time". The formula for <sub>n</sub>C<sub>r</sub> is n!/(n-r)!r!
	where "!" is the factorial symbol. Note that since "r' is indexed at zero,
	that is, the first row means r = 0, that means n, the exponent of the
	binomial expansion, will be n, but there will be n + 1 terms and
	therefore n +1 coefficients of Pascal's Triangle.</P>

	<p>Factorial n written n! means (n)(n-1)(n-2)...(1)</p>

	<p>By definition 0! = 1.</p>

	<P>For example, row 3 of Pascals Triangle means n=3 (third row
	of Pascals Triangle starting at 0) and r = 3; n is fixed but r
	will run from 0 to n, i,e, 0, 1, 2, and 3 in this example,
	so the coefficients of Pascal's Triangle are:</P>

	<ul>
	<li>3Cr = 3!/(3-r)!r! </li>
	<li>3C0 = 3!/(3-0)!0! = 6/6*1 = 1</li>
	<li>3C1 = 3!/(3-1)!1! = 6/2*1 = 3</li>
	<li>3C2 = 3!/(3-2)!2! = 6/1*2 = 3</li>
	<li>3C3 = 3!/(3-3)!3! = 6/1*6 = 1</li>
	</ul>

	<P>This program is written in JavaScript.</P>

	<P>By Mr. C. January, 2020</P>

	<P>*******************results******************************</P>

	<script>

	main(); //must call the main() function to run the program.
	function main() //Envelope program in main() function
	{ //start main() function block

	var ptrows = ""; // Pascal's Triangle rows, indexed at 0.

	// ask user to input the number of rowa
	ptrows = prompt("Enter rows of Pascals Triangle", "Type the value here");
	ptrows = parseInt(ptrows,10); //convert text input (string input) to an integer

	// Data Validation - Ensure user input is >= 0 for r.
	if(!(ptrows >= 0))
	{//start data validation if block
	document.write("<P>ptrows=", ptrows);
	document.write("<P>ptrows must be greater than or equal to zero");
	return; // stops execution of if block
	}//endof data validation if block

	document.write("<P><b>Pascals Triangle Coefficients</b></P>");
	document.write("<P>Number of Terms=", ptrows+1);
	document.write("<P>N= ", ptrows);

	// calculate the coefficients of each term
	for(let i = 0; i <= ptrows; i++)
	{ // start pt coefficient for loop
	var ptcoefficient = 0;
	ptcoefficient = nCr(ptrows,i);
	document.write("<P>r = ", i, " coefficient ", ptcoefficient );
	} // endof pt coefficient for loop

	}//endof main() function block

	// *****************************************************************************
	// function to return the factorial of any passed integer
	// note: the set of integers is abbreviated "Z"
	function factorial(_Z) // Z is set of integers, _Z means variable is an argument
	{ //start factorial function block
	var counter = _Z; // will use the integer argument as the starting value of a counter
	var factorialZ = 1;
	if(_Z === 0)
	{//start if _Z is 0 if block
	factorialZ = 1;
	return factorialZ;
	}//endof if _Z is 0 if block
	while (counter >= 1)
	{//start while block
	factorialZ = counter*factorialZ;
	counter = counter - 1;
	}//endof while block
	return factorialZ;
	} //endof factorial function block
	// *****************************************************************************

	// *****************************************************************************
	// function nCr to return the combination of n things taken r at a time
	function nCr(_n, _r)
	{ //start nCr function block
	var nMinusr = 0;
	var combinations = 0;
	nMinusr = _n - _r;
	combinations = factorial(_n)/((factorial(nMinusr))*factorial(_r));
	return combinations;
	} //endof nCr function block
	// *****************************************************************************

	// *****************************************************************************
	// function nPr to return the permutation of n things taken r at a time
	// TBD-use nCr for model
	// *****************************************************************************

	// *****************************************************************************
	// Console log variables for debugging - comment in/out as needed
	/*
	TBD
	*/
	// *****************************************************************************

	</script>

	<p><b>To check your answers, visit one of these sites:</b>
	<ul>
	<li><a href="http://mathforum.org/dr.cgi/pascal.cgi">Interactive Pascal's Triangle at MathForum.org</a></li>
	<li><a href="https://www.symbolab.com/solver/step-by-step/%5Cleft(x%2By%5Cright)%5E%7B5%7D">Binomial Expansion at Symbolab</a></li>
	<li><a href="http://ed.ted.com/lessons/the-mathematical-secrets-of-pascal-s-triangle-wajdi-mohamed-ratemi">Pascal's Triangle - Wajdi Mohamed Ratemi - TED Video</a></li>
	<li><a href="https://www.mathsisfun.com/algebra/binomial-theorem.html">The Binomial Theorem at MathIsFun.com</a><br><i>(check out the derivation of "Euler's Number" , aka "e".)</i></li>
	</ul>
	</p>

	</body>
	</html>