🍓 Euler's Dream Sandbox

⭕ Unit Circle Ballet

Watch as our orange stick figure dances around the unit circle! Drag the slider to change the angle θ, or press Play to watch the automatic animation.

The Magic Moment: When θ reaches π, watch for the spectacular collision that reveals Euler's famous identity!

∑ Taylor Series Builder

Build the Taylor series expansion term by term. Each time you click "Add Term", the stick figure carries a new term and adds it to the growing sum.

Watch the Convergence: See how the infinite series spirals toward the value -1 + 0i!

🎨 Symbol Sandbox

A playful mathematical playground! Click symbols to add them to the canvas, then drag them around. Watch for special interactions:

• Try spelling "EXIT" with symbols...
• Drop the stick figure on zero...
• Make π and i interact...
• Stack three i's together...

🎓 About Euler's Identity

e^(iπ) + 1 = 0

This beautiful equation links five fundamental mathematical constants: e (Euler's number), i (imaginary unit), π (pi), 1, and 0. It's been called "the most beautiful equation in mathematics"!