PresentationSusseccions
PresentationSusseccions
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PresentationSusseccions
Presentation of Susseccions available here http://futureun.github.io/PresentationSusseccionsOn Github FutureUN / PresentationSusseccions
Themes
Set your presentation theme: Black (default) - White - League - Sky - Beige - Simple Serif - Night - Moon - Solarized
Successions
Index
Abundant Numbers Leyland NumbersAbundant Numbers
What is it about?
Explanation of suseccion
Important functions used in the code
The final code
Abundant Number
What is?
In number theory, an abundant number is a number for which the sum of its proper divisors is greater than the number itself. The amount by which the sum exceeds the number is the abundance.
Take from Wikipedia
Example:
12 is an abundant number. Divisors: 1, 2, 3, 4, 6
Sum: 16
Abundance:4
16 Is grater than 12
Important functions used in the code (explanation)
Sum_of_div
<!--
int sum_of_div ( int n )
{
tmp.append(n);
int sum = 0;
for ( int i = 1; i < n ; i ++)
if ( n % i == 0 )
{
sum = sum + i;
tmp.append(i);
}
return sum;
}
-->
Code Processing:
<!--
//Better testing
ArrayList<IntList> abundants = new ArrayList <IntList>();
IntList tmp = new IntList();
int sum_of_div ( int n )
{
tmp.append(n);
int sum = 0;
for ( int i = 1; i < n ; i ++)
if ( n % i == 0 )
{
sum = sum + i;
tmp.append(i);
}
return sum;
}
// a comment to test git
void setup ()
{
size(576,442);
background(0,50,50);
int n = 10;
int cont = 0;
int number = 1;
while ( true )
{
if ( cont == n )
break;
tmp = new IntList();
int sumDiv = sum_of_div(number);
if ( number < sumDiv)
{
tmp.append(sumDiv);
abundants.add(tmp);
cont ++ ;
}
number ++ ;
}
for ( int i = 0 ; i < cont ; i ++ )
{
println (i + " " + abundants.get(i) );
}
float scale = 3;
float x = 0;
for ( int xi = 0 ; xi < 6 ; xi ++ )
{
float radOfSum = abundants.get(xi).get(abundants.get(xi).size() - 1 )/2.0;
x += radOfSum * scale;
float radOfNumber = abundants.get(xi).get(0)/2.0;
float y = radOfNumber * scale;
fill(255,255,200);
noStroke();
ellipse(x,y, radOfNumber * 2 * scale ,radOfNumber * 2 * scale);
y += radOfNumber* scale;
for ( int i = 1 ; i < abundants.get(xi).size(); i ++ )
{
int size = abundants.get(xi).size();
float diamOfActual =abundants.get(xi).get(i);
float diamOfFirst = abundants.get(xi).get(1);
float diamOfLast = abundants.get(xi).get(size - 2 ) * 1.1;
float a = map(diamOfActual,diamOfFirst
,diamOfLast,0,255);
fill(255,255-a,255-a);
noStroke();
y += diamOfActual/2.0 * scale;
//println(y);
ellipse(x, y , diamOfActual* scale,diamOfActual* scale);
y += diamOfActual/2.0 * scale;
}
x += radOfSum * scale;
}
}
-->
Code JavaScript:
<!--
var sketch = function ( p ) {
var n = 10;
var abundants = [];
var tmp = new Array();
function sum_of_div ( n )
{
tmp.push(n);
var sum = 0;
for ( var i = 1; i < n ; i ++)
if ( n % i == 0 )
{
sum = sum + i;
tmp.push(i);
}
return sum;
}
p.setup = function() {
p.createCanvas(576, 438);
p.noLoop();
}
p.draw = function () {
p.background(0,50,50);
// console.log("algo");
var cont = 0;
var number = 1;
//ellipse(30,30,30,30);
while ( true )
{
if ( cont == n )
break;
tmp = new Array();
var sumDiv = sum_of_div(number);
// console.log(sumDiv);
if ( number < sumDiv)
{
tmp.push(sumDiv);
//console.log(tmp);
abundants.push(tmp);
// console.log(abundants);
cont ++ ;
}
number ++ ;
}
var scale = 3;
var x = 0;
for ( var xi = 0 ; xi < 6 ; xi ++ )
{
var radOfSum = abundants[xi][abundants[xi].length - 1]/2.0;
x += radOfSum * scale;
var radOfNumber = abundants[xi][0]/2.0;
var y = radOfNumber * scale;
p.fill(255,255,200);
p.noStroke();
p.ellipse(x,y, radOfNumber * 2 * scale ,radOfNumber * 2 * scale);
y += radOfNumber* scale;
for ( var i = 1 ; i < abundants[xi].length; i ++ )
{
var length = abundants[xi].length;
var diamOfActual = abundants[xi][i];
var diamOfFirst = abundants[xi][1];
var diamOfLast = abundants[xi][length-2]*1.1;
var a = p.map(diamOfActual,diamOfFirst,diamOfLast,0,255);
p.fill(255,255-a,255-a);
p.noStroke();
y += diamOfActual/2.0 * scale;
p.ellipse(x, y , diamOfActual* scale,diamOfActual* scale);
y += diamOfActual/2.0 * scale;
}
x += radOfSum * scale;
}
}
};
var myp5 = new p5 (sketch, 'abundant_id');
-->
The result
Leyland Numbers
What is it about?
Explanation of suseccion
Important functions used in the code
The final code
Leyland numbers
What is?
In number theory, a Leyland number is a number of the form x^y + y^x where x and y are integers greater than 1.
This requirement is important, since without it every positive integer would be a Leyland number of the form x1 + 1x. Also, because of the commutative property of addition, the condition x ≥ y is usually added to avoid double-covering the set of Leyland numbers (so we have 1 < y ≤ x).
Take from Wikipedia
Example:
X=2 and Y=2 (x,y > 1)
X^Y + Y^X = 2^2 + 2^2 = 8
8 is the first leyland number
Important functions used in the code (explanation)
Pow
The best way to calculate the power of a number.
<!--
int pow(int n, int p)
{
if(p==0) return 1;
else if ( p % 2 == 1 )
return n * pow(n,p-1);
int a = pow ( n , p%2);
return a * a;
}
-->
Important functions used in the code (explanation)
leyland
<!--
IntList v;
IntList leyland (int n)
{
if (n>13)
n=13;
v=new IntList();
enesimo= new IntList();
for(int i=0;i<n;i++)
for(int j=0;j<=n-i;j++)
{
int m = ( pow(i+2,j+2) + pow(j+2,i+2) );
if(! v.hasValue(m) )
v.append(m);
}
//println(v);
v.sort();
//println(v);
for(int i=0;i<n;i++)
enesimo.append(v.get(i));
return enesimo;
}
-->
Code Processing:
<!--
IntList v;
IntList enesimo;
int pow(int n, int p)
{
if(p==0) return 1;
else if ( p % 2 == 1 )
return n * pow(n,p-1);
int a = pow ( n , p/2);
return a * a;
}
IntList layland (int n)
{
if (n>13)
n=13;
v=new IntList();
enesimo= new IntList();
for(int i=0;i<n;i++)
for(int j=0;j<=n-i;j++)
{
int m = ( pow(i+2,j+2) + pow(j+2,i+2) );
if(! v.hasValue(m) )
v.append(m);
}
//println(v);
v.sort();
//println(v);
for(int i=0;i<n;i++)
enesimo.append(v.get(i));
return enesimo;
}
void setup()
{
background(0);
//ellipse(200,200,55,55);
size(400,400);
int n = 12;
IntList lay =layland(n);
IntList layr = layland(n);
layr.sortReverse();
for(int i=0;i<lay.size();i++)
{
float a = map (layr.get(i),lay.get(0),layr.get(0),lay.get(0),width+width/4);
float b = map (lay.get(i),lay.get(0),layr.get(0),0,255);
fill(b,0,0);
noStroke();
ellipse(width/2,height/2,a,a);
}
}
-->
Code JavaScript:
<!--
var circles= 10;
function setup() {
createCanvas(400, 400);
noLoop();
}
function draw() {
background(0);
var lay = leyland();
var layr = leyland();
layr.reverse();
for(var i=0;i<circles;i++)
{
var a = map(layr[i],lay[0],layr[0],lay[0],width+width/4);
var b = map(lay[i],lay[0],layr[0],0,255);
//console.log(lay);
noStroke();
fill(b,0,0);
ellipse(width/2,height/2,a,a);
}
}
function pow(n, p)
{
if(p==0)
return 1;
else
return n * pow(n,p-1);
}
function leyland()
{
var myset = new Set();
for(var i=0; i<circles;i++)
for(var j=0;j<circles-i;j++)
{
var m = (Math.pow(i+2,j+2) + Math.pow(j+2,i+2));
myset.add(m);
}
//console.log(myset);
var arr = Array.from(myset);
arr.sort(CompareNumbers);
//console.log(arr);
return arr.slice(0,circles);
}
function CompareNumbers(a, b){
return a-b;
}
-->
The result
Themes
Set your presentation theme:
Black (default) -
White -
League -
Sky -
Beige -
Simple
Serif -
Night -
Moon -
Solarized