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Pi

Pi, or $\pi$, is commonly used in the context of circles in geometry. In particular, the circumference $C$ of a circle that has a diameter $d$ is $C = \pi d$. Also, the area $A$ of a circle with radius $r$ is $ A = \pi r^2$. Note that $2r = d$. This is how…

Prime Number

What is a prime number? A prime number cannot be divided by another number, with the exception of the number 1 and the number itself. Some prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and 23. Prime numbers are involved in encryption in today’s technology. Some people think that prime numbers are…

Pythagoras Theorem

What is the Pythagoras theorem? It is $ a^2 + b^2 = c^2$. Here, $a$, $b$ and $c$ are the lengths of a right triangle. Note that $c$ is the hypotenuse of the right triangle. A right triangle has an angle of 90 degrees.

Bubble Sort Algorithm in Python

In this post, I provide a code that performs a bubble sort in python. Before using, I recommend checking the indentations, as this code was written in a standard text-editor. This python bubble-sort algorithm should be fine, though. This python algorithm was written using the example output in Reference 1. One can compare the output of…

Conservation of Momentum

If an external force is not applied to a system, then momentum is conserved. For example, consider one dimensional motion, and suppose there are two objects $A$ and $B$ with masses $m_A$ and $m_B$, respectively. If the initial velocity of object $A$ is $v_{A_i}$ and the initial velocity of object $B$ is $v_{B_i}$, then $m_A…

Newton’s Second Law

Newton’s Second Law is symbolically written as $ \vec{F}_{net} = m \vec{a}$. Here, $\vec{F}_{net}$ is the net force on an object with nonzero mass $m$. If the object has a mass of zero, such as a photon, Newton’s second law indicates that the net force on the object would be the zero vector. If the…

Simple Interest and Compound Interest

Here is a series of videos I made about simple interest and compound interest. Simple Interest and Compound Interest Semiannual Interest A Special Case of the Compound Interest Formula

Discovery of the Logarithm by John Napier

Here is a short series of videos I made about the discovery of the Logarithm. John Napier is credited with the discovery of the logarithm, and Leonhard Euler developed the logarithm used today. The contents of the following videos are based on Reference 1. Part 1 Part 2 Part 3 Part 4 References [1] e, The…

Investigating the Meaning of a Function to the Right of the Del Operator

Let $F(x,y,z) \equiv f(x) g(y) h(z)$. In this previous post, $\vec{\nabla}F(x,y,z)$ was written in terms of spherical coordinates and unit vectors for a spherical coordinate system. The corresponding equation was found to be $ \vec{\nabla}F(x,y,z) = \vec{e}_r \frac{\partial F(x,y,z) }{\partial r} + \vec{e}_\theta \frac{1}{r} \frac{\partial F(x,y,z) }{\partial \theta} + \vec{e}_\phi \frac{1}{r\sin\theta} \frac{\partial F(x,y,z) }{\partial \phi} $. This is (6)…

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