Mathematics is everywhere, a small equation you studied in your childhood become a big reason for many changes in engineering and technology around the world. In 2013, famous author Ian Stewart published a bookPythagoras’s Theorem World. This book elaborately explains each equation and how it molded engineering to human accessible Pythagoras’s Theorem, we are going to see the summery of that 10 Equations and its applications.
1. Pythagoras’s Theorem
The Pythagorean Theorem is a statement in geometry that shows the relationship between the lengths of the sides of a right triangle – a triangle with one 90-degree angle.
2. Logarithms
A logarithm is the power to which a number must be raised in order to get some other number .
Applications of Logarithms
Logarithms widely used to measure Earthquake intensity measurement, Acid measurement of solutions(pH Value), Sound intensity measurements, and express larger value.
3. Calculus
Calculus is a form of mathematics which was developed from algebra and geometry. It is made up of two interconnected topics, differential calculus, and integral calculus.
Applications of Calculus
Calculus is widely used for engineers, scientists, and economists. The contribution of these professionals has a huge impact on our daily life – from your microwaves, cell phones, TV, and car to medicine, economy, and national defense.
4. Law of Gravity
Every object in the Universe attracts every other object with a force directed along the line of centers for the two objects that is proportional to the product of their masses and inversely proportional to the square of the separation between the two objects.
The significance of Gravitational Laws:
Gravitational laws are used in many ways from small bicycle manufacturing to the aerodynamics of a Rocket.
5. The Square Root of Minus One
Imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1.
The significance of the Imaginary number
When we get the square root of -1, we replace it with the shortcut i, which is called the "imaginary" number because negative square roots don't actually exist (and it's much easier to keep writing i than to write out the square root every time). That way, we keep the "imaginary" number just in case we will make the number useful again later in another equation by squaring it or multiplying it by a different imaginary number or something. And it turns out, in EE, this happens all the time.
6. Euler’s Formula for Polyhedra
A (convex) polyhedron is called a regular convex polyhedron if all its faces are congruent to a regular polygon, and all its vertices are surrounded alike. Plain experimentation with sticks will allow you to easily construct 5 regular polyhedra: tetrahedron, cube, octahedron, icosahedron, and dodecahedron.
7. Normal Distribution
The normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
8. Wave Equation
The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in classical physics—such as mechanical waves (e.g. water waves, sound waves and seismic waves) or light waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics.
A pulse traveling through a string with fixed endpoints as modeled by the wave equation.
Spherical waves coming from a point source.
A solution to the 2D wave equation
9. Fourier Transform
The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.
Applications of Logarithms
Logarithms widely used to measure Earthquake intensity measurement, Acid measurement of solutions(pH Value), Sound intensity measurements, and express larger value.
10. Navier – Stokes Equation
Navier Stokes equation is used to describe the flow characteristics of a Newtonian fluid. A fluid in which relation between stress and rate of strain is linear. In other words, a fluid obeys Newton law of viscosity. Honey, Benzene, Water, Kerosene oil, are just a few examples of a Newtonian fluid.
10. Navier – Stokes Equation
This equations arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscousterm (proportional to the gradient of velocity) and a pressure term hence describing viscous flow.
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