Infinite Limits

What is the Rocket Equation? The rocket equation is a fundamental principle in physics, based on Newton’s Third Law of Motion) that describes the motion of rockets in space. It is a mathematical formula that calculates the velocity of a rocket based on its mass, the mass of the propellant it carries, and the speed at which it expels that propellant. Credit: NASA   The equation shows that as the mass of the rocket decreases (as it expels propellant), its velocity increases. This is because the rocket's momentum is conserved, and as the mass decreases, the velocity must increase to maintain momentum. The rocket equation is important because it determines the amount of propellant required to achieve a certain velocity or distance in space. It also shows that there are limits to the performance of rockets, as increasing the propellant mass requires a corresponding increase in the initial mass of the rocket, which makes it heavier and more difficult to launch. Credit: The Planetary Soci...

  Technical analysis is a trading methodology used to evaluate securities and financial markets based on statistical trends and market activity. Technical analysts examine past market data, including price and volume, to forecast future market behavior and make investment decisions. In this blog, we will explore the basic concepts and tools used in technical analysis. The Basics: Price charts The cornerstone of technical analysis is the price chart. Technical analysts use charts to visualize historical prices and volume of a security over a specific period. These charts are available in various formats, including line charts, bar charts, and candlestick charts. Line charts are the simplest type of chart, displaying the security's closing prices over a given period. Bar charts add more detail by showing the open, high, low, and close prices of the security in a given time frame. Candlestick charts, the most popular type of chart, show the same information as a bar chart but are easi...

The Mandelbrot Set is a set of complex numbers commonly used in art, due to its mathematical beauty. It was first defined by Robert W. Brooks   and Peter Matelksi in 1978, and the first visualisation was made by Benoit Mandelbrot in 1980.   Credit: American Scientist A lot of websites, videos, applets, and so on do a repeated zoom into the boundary of the Mandelbrot Set. But in mathematical terms, we define the Mandelbrot Set as the set of complex numbers which (under iteration) stays bounded within two. Here’s how it’s mathematically represented (don’t skip this, it’s easy math): f c (z) = z 2 + c, f c (z)<= 2 Let’s take an example here to understand this.   If c=-2,   f -2 (0) = 0 2 + (-2) = -2 (You start with z=0 as default) f -2 (-2) = (-2) 2 + (-2) = 4+ (-2) = 2 (You take the result of the previous function and input it as z in the next iteration) f- 2 (2) = (2) 2 + (-2) = 4+ (-2) = 2 We know that the result of the previous function (2), upon another itera...