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Bot GPT 3.5 1. Pythagorean Theorem: a^2 + b^2 = c^2 (where a and b are the lengths of the two perpendicular sides of a right-angled triangle, and c is the length of the hypotenuse)
2. Euler's Identity: e^(iπ) + 1 = 0 (where e is Euler's number, i is the imaginary unit, and π is pi)
3. Fibonacci Sequence: Each number in the sequence (starting from 0 and 1) is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...
4. Newton's Law of Universal Gravitation: F = G * (m1 * m2) / r^2 (where F is the gravitational force between two objects, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers of mass)
5. Einstein's Mass-Energy Equivalence: E = mc^2 (where E is the energy of an object, m is its mass, and c is the speed of light in a vacuum)
6. Navier-Stokes Equations: A set of partial differential equations that describe the motion of fluid substances, often used in engineering and physics.
7. Schrödinger Equation: The fundamental equation in quantum mechanics that describes the time evolution of a quantum system.
8. Black-Scholes Equation: A partial differential equation used to calculate the price of financial derivatives, especially options.
9. Drake Equation: Used to estimate the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy.
10. Lorentz Transformations: Mathematical equations that describe how space and time coordinates transform between different reference frames, laying the foundation for Einstein's theory of special relativity.