# 5 Fascinating Facts About Triangles That Will Surprise You

If you have enjoyed the wonders and beauty of mathematics shown in this blog, here are some addition for you to appreciate it more. Below are some of the most amazing facts about triangles.

1. The three altitudes of meet at a common point. This point is called the orthocenter of the triangle.

2. The three lines from each vertex to the midpoint of the opposite side also meet at a common point called centroid of the triangle. Continue reading

# Deceptive and Misleading Mathematical Patterns

In the Mathematical Palette, I have mentioned about mathematics as a science of patterns.   I have highlighted that some mathematical patterns are obvious, some can be solved mathematically, and some are a bit counter-intuitive.

Venus Transit (2004)

In reality, we have improved our way of living by recognizing and generalizing patterns. For example, we are able to predict the weather through the data we have collected all over the years. We look for patterns from the data and use probability to announce that there will be rain showers and thunderstorms for the next three days and feel pretty sure about it. Through patterns, we have even predicted the movement of planets. We know that the next transit of Venus  is  in 2117 (too bad if you didn’t see it on June 5).  That is how beautiful and powerful patterns are. Continue reading

# Complex Numbers and their Properties

Imaginary numbers as we have discussed in Tuesday’s post are numbers of the form bi where $b$ is a real number and $i = \sqrt{-1}$. The term imaginary as (opposed to real) was first used by Rene Descartes, the mathematician who invented Coordinate Geometry — the Cartesian plane in particular.  Leonhard Euler was the one who introduced the symbol $i$ for $\sqrt{-1}$.

Leonhard Euler

Gerolamo Cardano, a pioneer in probability, was the one who suggested the   use of numbers of the form $a + bi$ where $a$ and $b$ are real numbers and $i = \sqrt{-1}$.  Numbers of this form were named complex numbers by Carl Frederich Gauss.The real part of $a + bi$ is $a$ and the imaginary part is bi. Continue reading