Published in Recreational maths·2 days agoMember-onlyParabola focus and directrixA parabola can be defined in terms of parametric equations or alternatively in Cartesian form. An alternative way to define a parabola is as a locus of points. we will look at that form in this article. Focus and directrix The locus defining a parabola depends on a focus and a directrix. The…Pure Mathematics4 min readPure Mathematics4 min read
Published in Recreational maths·Nov 12, 2022Member-onlyMaclaurin series of the exponential functionIn this article we will use the Maclaurin series to find a polynomial approximation to the exponential function, e^x. The general formula for the Maclaurin series for the function f(x) is:Maclaurin Series4 min readMaclaurin Series4 min read
Published in Recreational maths·Nov 6, 2022Member-onlySolving equations using the Newton-Raphson methodThe Newton-Raphson method is a numerical method to solve equations of the form f(x) = 0. This method requires us to also know the first differential of the function. But the Newton-Raphson method has very good convergence, so it can often provide an accurate result very quickly. Example — square root of two using Newton-Raphson method As a simple…Mathematics7 min readMathematics7 min read
Published in Geek Culture·Oct 14, 2022Member-onlyPong game using Pygame — step 3This is the third article in a series where we will develop a complete game of Pong using Pygame. In the previous steps: step 1, we created a window and displayed the bat and ball, with no animation. step 2, we animated the ball, making it bounce off the 4…Python5 min readPython5 min read
Published in Geek Culture·Oct 8, 2022Member-onlyPong game using Pygame — step 2Second installment in the saga. This is the second article in a series where we will develop a complete game of Pong using Pygame. In the previous step, we created a window and display the bat and ball, with no animation. In this step we will animate the ball, making…Python11 min readPython11 min read
Published in Geek Culture·Oct 4, 2022Member-onlyCustom image processing with NumPyUse the power of NumPy to write your own image processing code. In this article, we will learn how to use NumPy to store and manipulate image data. We will use the Python Imaging Library (PIL) to read and write data to standard image file formats. This article explains how…Python5 min readPython5 min read
Published in Geek Culture·Sep 30, 2022Member-onlyHow is NumPy so damn fast?Short answer, it’s written in C, longer answer… When we talk about the efficiency of NumPy arrays (np arrays), what exactly do we mean? There are two separate issues: Efficiency of memory usage. Processing efficiency. Why are NumPy arrays more efficient than Python lists? The basic reason NumPy is more efficient is that it is written in C rather…Python7 min readPython7 min read
Published in Geek Culture·Sep 27, 2022Member-onlyPong game using Pygame — step 1First in a series of pygame articles This is the first article in a series where we will develop a complete game of Pong using Pygame. In this step, we will simply create a window and display the bat and ball, with no animation. The code for this article can…Python8 min readPython8 min read
Published in Geek Culture·Sep 19, 2022Member-onlyLooping over two lists with zipA Pythonistic technique to avoid loop counters We sometimes need to loop over two different sequences at the same time. For example, if we had two lists: colors = ["red", "green", "blue"] shapes = ["circle", "square", "triangle"] and we wanted to print these lists side by side: red circle green square blue…Python5 min readPython5 min read
Published in Geek Culture·Sep 18, 2022Member-onlyDitch loop counters, use this insteadWrite more pythonic code with enumerate Even though it is often best to avoid loop counters, there are times when they can be useful. Fortunately, you don’t have to forget everything you have learnt so far — you can use the enumerate function. …Python4 min readPython4 min read
