Mathematics

Logic is the foundation of everything. Here we derive the fundamental truths of geometry, algebra, and calculus.

Geometry

• Area of a Circle - Why is it \(\pi r^2\)?
• Triangle Area - Why base times height divided by 2?
• Volume of a Sphere - Deriving \(\frac{4}{3}\pi r^3\).
• Pythagorean Theorem - A geometric proof.

Fundamentals

• Long Division - Understanding the place value algorithm.
• Order of Operations - Why PEMDAS works and common pitfalls.
• Decimal to Fraction Conversion - From terminating to repeating decimals.
• Percentage Changes - Why successive changes don't add up.
• Rounding and Significant Figures - Tracking precision through calculations.
• Dividing Fractions - Why do we flip and multiply?
• Negative times Negative - Why is the result positive?
• Exponent Rules - Why is \(x^0 = 1\)?
• Distributive Property - How it works with subtraction.

Analysis & Transforms

• Fourier Transform - Decomposing any signal into frequencies.