
Dirac Equation
 How particles (like electrons) behave when they travel close to the speed of light.

Combine 2 important ideas
 Quantum Mechanics
 Theory of Relativity
 Cornerstones of Modern Physics
 Predict existence of antimatter.

Euler's Identity
 Link all of the constants of mathematics together.

Basic mathematical operations
 Addition
 Multiplication
 Exponentiation
 Mozart of Mathematics

Pi
 How circumference of a circle varies with its diameter.
 Irrational number, digits go on forever without repeating.

Usage
 GPS
 Geometry

Einstein's Field Equation
 How the Universe works at most fundamental level.
 Changed the understanding of nature and evolution of the Universe.
 Earliest moments of creation.
 Predict the existence of black holes and gravitational waves.

Bayee's Theorem
 Calculate the probability that one event (A) is true, given that another event (B) is also true.
 Underlie rational thinking and decision making, rather than because of any intrinsic aesthetic appeal.

Usage
 Detect faults
 Surveillance
 Military Defence
 Searchandrescue
 Medical screening

Riemann's Formula

Calculate the number of primes below a given number.
 25 Primes between 1 and 100.
 Deeper rule governing which numbers are prime.
 Primes are controlled by zeta function

Usage
 Message security in codes
 Unlock the secrets of prime numbers

the Logistic Map

Model natural processes
 Population
 Animal grows and shrinks
 Example of Chaos History
 Great complexity may arise from very simple rules.

A "Simple" Arithmetic Progression
 A sequence of numbers separated by the same amout.
 Algorithmic Reduction
 Symmetric

Hamilton's Quaternion Formula
 Work with complex numbers that include the square roots of negative numbers.
 Quaternion algebra

Usage
 Describe objects orientations on the screen.
 Computer graphics industry

the Wave Equation

Describe how waves behave.
 Sound
 Vibrations
 Light
 Radio Waves

Study on phenomena
 Earthquakes
 Oil prospecting
 Safety on ships
 Start from a violin string.

The YangBaxter Equation
 Explain mathematical theory of knots

Implications for Mathematics and physics
 Waves in shallow water
 interaction of subatomic particles
 mathematical theory of knots
 String theory

The EulerLagrange Equation
 Describe how a rocket would go around a black hole.
 Express classical physics simply whithin a single framework.
 Deceptively short and simple
 Shape of a soap bubble
 Main Topic 13
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