And now for my funny comment:
If math was a sport, this hyperbola would be doing acrobatics while the cycloid is rolling with laughter.
Javascript Code
// Title: Hyperbolic Artistry with a Side of Cycloid
// First, we create our canvas and context
// Set canvas background to white for clarity
ctx.fillStyle = 'white';
ctx.fillRect(0, 0, 512, 512);
// Constants for the hyperbola
const angle = 70 * (Math.PI / 180); // convert 70 degrees to radians
const pDistFromFirstAsymptote = 30;
const pDistFromSecondAsymptote = 36;
const asymptotePointDist = Math.sqrt(pDistFromFirstAsymptote ** 2 + pDistFromSecondAsymptote ** 2);
// Calculate intersection point of asymptotes
const centerX = 512 / 2;
const centerY = 512 / 2;
// Calculate slope of asymptotes
const slope1 = Math.tan(angle / 2);
const slope2 = -slope1;
// Function to draw asymptotes
function drawAsymptotes() {
ctx.strokeStyle = 'lightgray';
ctx.beginPath();
ctx.moveTo(0, centerY - centerX * slope1);
ctx.lineTo(512, centerY + (512 - centerX) * slope1);
ctx.moveTo(0, centerY - centerX * slope2);
ctx.lineTo(512, centerY + (512 - centerX) * slope2);
ctx.stroke();
}
// Function to draw the hyperbola
function drawHyperbola() {
const a = asymptotePointDist / (2 * Math.sqrt(2)); // Semi-major axis
const b = a * Math.sqrt(Math.tan(angle / 2) ** 2); // Semi-minor axis
ctx.strokeStyle = 'black';
for (let x = -a; x <= a; x += 0.1) {
const y = b * Math.sqrt(1 + (x / a) ** 2);
ctx.beginPath();
ctx.arc(centerX + x, centerY + y, 0.5, 0, 2 * Math.PI);
ctx.stroke();
ctx.beginPath();
ctx.arc(centerX + x, centerY - y, 0.5, 0, 2 * Math.PI);
ctx.stroke();
}
}
// Function to draw the tangent and normal
function drawTangentNormal() {
const x = 20; // a convenient x-coordinate for our tangent and normal
const y = b * Math.sqrt(1 + (x / a) ** 2);
// Tangent
const tangentSlope = (b ** 2 * x) / (a ** 2 * y);
ctx.beginPath();
ctx.strokeStyle = 'blue';
ctx.moveTo(centerX + x - 50, centerY + y - 50 * tangentSlope);
ctx.lineTo(centerX + x + 50, centerY + y + 50 * tangentSlope);
ctx.stroke();
// Normal
const normalSlope = -1 / tangentSlope;
ctx.beginPath();
ctx.strokeStyle = 'green';
ctx.moveTo(centerX + x - 50, centerY + y - 50 * normalSlope);
ctx.lineTo(centerX + x + 50, centerY + y + 50 * normalSlope);
ctx.stroke();
}
// Function to draw a cycloid
function drawCycloid() {
const r = 20; // radius of the rolling circle
const step = 0.1; // smaller step means smoother curve
ctx.beginPath();
ctx.strokeStyle = 'red';
for (let t = 0; t < 4 * Math.PI; t += step) {
const x = r * (t - Math.sin(t));
const y = r * (1 - Math.cos(t));
ctx.lineTo(512 / 2 + x, 512 / 2 + y);
}
ctx.stroke();
}
// Now we call our functions to draw the hyperbola and cycloid
// And now for my funny comment:
// If math was a sport, this hyperbola would be doing acrobatics while the cycloid is rolling with laughter.
AI
Model: gpt-4-1106-preview
Time: 41 seconds
Prompt Tokens: 497
Completion Tokens: 919
Total Token Cost: 1416
balloon party
beautiful beach
cute puppy dog
happy cat
house