Mathematics in nature - a creative essay topic really.
1. Shadow lengths due to sun rays falling on trees, buildings, people
2. Dispersion angles of 40 to 42 deg. of sun rays falling on small droplets of water suspended in atmosphere after a rain. This creates a rain bow.
3. Total internal reflection - mirage - in deserts. Critical angle.
4. Spherical shape of planets - a shape has least surface area for a given volume - due to gravitation. Earth, moon etc.
5. Water surface on top of a water body being a horizontal two dimensional plane.
6. Natural (in water) waves - in Sine and Cos wave shape.
7. Tree trunks in nearly cylindrical shape in many trees - to minimize the surface area for a given volume. This is to minimize water dissipation.
8. Conical shape of mountains or peaks