Tag Archives: Algebra

Method of Exhaustion

Method of Exhaustion

Eudoxus, a Greek mathematician 408-355 BC, developed the idea of seeking mathematical solutions using the $\textit{Method on Exhaustion}$: at this stage, you achieve a more accurate figure. For example, he produced a ladder of numbers to find an increasingly accurate solution to $\sqrt{2}$. Starting with $1$ and $1$ as the first row, he added those […]

The Golden Ratio

The Golden Ratio

Since the days of old, artists, as well as mathematicians, have known that there is a special, aesthetically pleasing rectangle with width $1$, length $x$, and the following property:When a square of side $1$ is removed, the remaining rectangle has the same proportions as the original rectangle. Since the new rectangle has a width $x-1$ […]

Index Notation

Index Notation

A convenient way to write a product of $\textit{identical factors}$ is to use $\textbf{exponential}$ or $\textbf{index notation}$.Rather than writing $5 \times 5 \times 5 \times 5$, we can write this product as $5^4$. The small $4$ is called the $\textbf{exponent}$ or $\textbf{index}$, and the $5$ is called the $\textbf{base}$.If $n$ is a positive integer, then […]

Surd Equations Reducible to Quadratics

Surd Equations Reducible to Quadratics

Surd Equations Reducible to Quadratic for Math Algebra is done squaring both sides for removing surds and radical expressions. Make sure to check whether the solutions are correct by substituting them into the original surd equations. Question 1 Solve \( x = \sqrt{x+2} \). \( \begin{aligned} \displaystyle \require{AMSsymbols} \require{color}x^2 &= x+2 &\color{red} \text{square both sides} […]