We examine the double-angle and triple-angle formulas and derive them from the Trigonometric Addition Formulas. We also derive the half-angle formulas from the double-angle formulas.

Examine the definitions of trigonometric functions and the relationships between them, and derive the addition formulas for trigonometric functions and their derivative formulas.

This post covers designing prompts for multilingual translation of markdown text files, and automating the process with Python using an API key from Anthropic and the designed prompt. This is the f...

Exploring the necessity of writing good code and the key principles for writing good code in general.

Let's explore the concept of technical debt, why it occurs, and how to minimize it.

Let's calculate the macroscopic cross-section of a homogeneous mixture containing two or more nuclides.

Calculate the intensity of a neutron beam as it passes through a target material based on penetration distance, and derive the mean free path of neutrons from this calculation.

Neutrons, being electrically neutral, can pass through the electron cloud of atoms without electrical influence and directly interact with atomic nuclei. We explore the types of neutron interaction...

We explore the Bernoulli equation and its solution method, as well as the logistic equation, which is a special form of the Bernoulli equation.

We explore the relationship between decay constants, half-lives, and mean lifetimes of radioactive nuclides, and calculate the radioactivity of radioactive nuclides at any given time t in a given d...