Pythagorean Proof

ReturningValues/ReturningValues.pde

@@ -1 +1,69 @@
+//declare theta
+float theta;
 
+void setup() {
+  //set size
+  size(500, 500);
+}
+
+//definies float c as the hypotenuse of a right triangle with sides a and b
+float c(float a, float b) {
+  return sqrt(sq(a)+sq(b));
+}
+
+void draw() {
+  //draw background
+  background(0);
+
+  //set modes, initial stroke, initial text size
+  rectMode(RADIUS);
+  noStroke();  
+  textSize(15);
+
+  //define theta 
+  theta = asin(mouseX/(c(mouseX,width-mouseX)));
+
+  pushMatrix();
+    translate(width/2,height/2);
+    rotate(theta);
+    fill(255);
+    rect(0,0,c(mouseX,width-mouseX)/2,c(mouseX,width-mouseX)/2);
+    fill(0);
+    pushMatrix();
+      translate(0,20-c(mouseX,width-mouseX)/2);
+      rotate(-theta);
+      text("c", 0,0);
+    popMatrix();
+
+    pushMatrix();
+      translate(20-c(mouseX,width-mouseX)/2,0);
+      rotate(-theta);
+      text("c", 0,0);
+    popMatrix();
+
+    pushMatrix();
+      translate(0,c(mouseX,width-mouseX)/2-20);
+      rotate(-theta);
+      text("c", 0,0);
+    popMatrix();
+
+    pushMatrix();
+      translate(c(mouseX,width-mouseX)/2-20,0);
+      rotate(-theta);
+      text("c", 0,0);
+    popMatrix();
+
+    pushMatrix();
+      rotate(-theta);
+      textSize(30);
+      text("c²", 0,0);
+    popMatrix();
+  popMatrix();
+
+  //set stroke and draw line to cursor to indicate what controls the values
+  stroke(255,0,0);  
+  line(mouseX,0,mouseX,mouseY);
+
+  //print values and proof
+  println("a = " + mouseX + ", b = " + (width-mouseX) + ", c = " + round(c(mouseX, width-mouseX)) + ". (a + b)² = a² + 2ab + b². c² = (a + b)² - 2ab.");
+}

VoidFunctions/VoidFunctions.pde

@@ -1 +1,63 @@
+//declare variables
+int weight = 2;
+float x;
+float y;
+float diam = 10;
+int total = 50;
+PVector [] lag = new PVector[total];
 
+void setup() {
+  //set size and strokeweight
+  size(500, 500);
+  strokeWeight(weight);
+
+  //set lag values initially so that they are not visible
+  for (int i = 0; i < total; i++) {
+    lag[i] = new PVector(-diam-weight*total, -diam-weight*total);
+  }
+}
+
+//define square function to include color
+void square(float c1, float c2, float c3, float alpha) {
+  fill(c1, c2, c3, alpha);
+  rect(width/2-25, height/2-25, 50, 50);
+}
+
+//define circle function to include position, diameter, color
+void circle(float x, float y, float diam, float c1, float c2, float c3, float alpha) {
+  fill(c1, c2, c3, alpha);
+  ellipse(mouseX, mouseY, diam, diam);
+}
+
+void draw() {
+  //draw background
+  background(0);
+
+  //define x as mouseX in case mouse moves within frame
+  x = mouseX;
+  y = mouseY;
+
+  //set stroke and draw square
+  stroke(255);
+  square(255, 255, 255, 128);
+
+  //remove fill for ripples
+  noFill();
+
+  //shift values for lag
+  for (int i = 0; i < total-1; i++) {
+    lag[i].set(lag[i+1]);
+  }
+
+  //set final lag to mouse position
+  lag[total-1].set(x, y);
+
+  //draw all ripples at location
+  for (int i = 0; i < total; i++) {
+    stroke(255, 255*i/(total-1));
+    ellipse(lag[i].x, lag[i].y, diam+weight*(total-1-i), diam+weight*(total-1-i));
+  }
+
+  //draw circle
+  circle(x, y, diam, 255, 0, 0, 128);
+}