Words and Buttons Online

This is the source code for Words and Buttons Online — a growing collection of interactive tutorials, guides, and quizzes about maths, algorithms, and programming.

Tags

#algorithms #demos #mathematics #programming #quizzes #tutorials

Pages

• Complex numbers and conformal mapping This explains the geometry of complex numbers. Explains conformal transformations, introduces analytic functions, and shows that analytic complex functions are conformal. And using the connection between the geometry and the analysis explains it all in just some five minutes. ^{#mathematics #tutorials}

• Lagrange polynomial as a gateway drug to basis splines This explains Lagrange interpolation: what is the Lagrange polynomial, why does it run through all the points, what is the basis polynomial, and how come it's a polynomial in the first place. ^{#mathematics #tutorials}

• Trippy polynomials in arctangent scale This shows the global properties of polynomials, their derivatives, and explains how the Maclaurine and Taylor series work all with animated plots in arctangent scale. ^{#mathematics #tutorials}

• Partial order and non-Boolean logic Non-Boolean logics are rare but not extinct. Interval logic is one example. Sometimes, you can implement a logic you want within total order or partial order but sometimes even that isn't enough and you need an even more general relation. With operator overloading, you have the freedom to go there but you also have less assurance when working within the total order. ^{#mathematics #tutorials}

• Yet another alternative to floating-point numbers This shows how computable intervals written in rational bounds may not only account for the input error but keep computational error under control as well. ^{#mathematics #programming #quizzes}

• Why is it ok to divide by 0.0? This explains why dividing by zero in floating-point numbers is ok. ^{#mathematics #programming}

• Can we use lemniscates for ultra-cheap vector graphics? This depicts an old idea of using multifocal lemniscates to draw arbitrary shapes. In some applications, this may be indeed an economical alternative to splines. ^{#demos #mathematics}

• Bi-whatever transformations An interactive explanation of how polynomial transformations such as trilinear or biquadratic or even linear-cubic work, and how to craft your own. ^{#demos #mathematics}

• Arctangent scale. It's like the logarithmic scale but infinite An interactive demo of how, with arctangent used as a scale, we can show any function on a screen. And not just a fragment of it but the whole function. ^{#demos #mathematics}

• Image darning A simple image processing algorithm that cleans up dirt stains from old newspapers. I called it “darning” because of how it works. ^{#algorithms #demos #mathematics}

• Error codes are not numbers. But they are. Can we exploit that? An interactive explanation of how we can use floating-point NaNs as error code holders in C++. ^{#demos #mathematics #programming}

• Binary search An interactive demo of the binary search algorithm along with its one slightly more obscure but promising variant. ^{#algorithms #tutorials}

• Honeycomb texture generator This generates honeycomb textures of a special quasi-irrational form. Explanation included. ^{#demos #mathematics}

• Sine and cosine A pair of interactive mnemonics for sine and cosine. There are also examples of practical usage. Basically, the second half of a tutorial is about how the first half was made. ^{#mathematics #tutorials}

• Challenge your performance intuition with nanosecond sorting And yet another interactive quiz where you get to estimate the performance difference between several variants of the same code. ^{#programming #quizzes}

• SWInE: Simplicial Weight Interpolation and Extrapolation An alternative to splines nobody knows about. The localization of Shepard's method for a simplicial complex. ^{#demos #mathematics}

• Quadratic splines are useful too This explains simple quadratic splines, how to craft one yourself, and why. ^{#demos #mathematics}

• Circles and lines vs. polynomial splines An alternative to polynomial splines. Smooth parametric curves made from arcs and line segments. ^{#demos #mathematics}

• SymPy makes math fun again An introduction into symbolic computations in Python. Don't worry, it's much simpler than it sounds. It's about making Python do your math for you with very little investment in the technology. ^{#mathematics #programming #tutorials}

• Yet another floating-point tutorial Most of what you should know about floating-point numbers put together in an interactive tutorial with quests and puzzles. ^{#mathematics #programming #tutorials}

• Lexical differential highlighting instead of syntax highlighting This type of highlighting is ideal for assembly. With it, the things that shouldn't seem similar usually don't. ^{#demos #programming}

• Interactive mnemonics for dot and cross vector products Just a pair of mnemonics for dot and cross vector products. They present the functions, show how they work, and why one is dot and the other is cross. ^{#mathematics #tutorials}

• Simple image vectorization This is an example of an image vectorization algorithm. It shows the bilinear interpolation, polynomial approximation, differential analysis, and iterative algorithms working together to solve a practical problem ^{#algorithms #demos #mathematics}

• The simplest possible smooth contouring algorithm A 3-part smooth contouring algorithm that shows partial derivatives, gradients, and parametric polynomials working together. ^{#algorithms #demos #mathematics}

• Using logical operators for logical operations is good This is the follow-up for the “Challenge your intuition with C++ operators”. It shows that despite the occasional gains from a better compilation, using the proper operators is still beneficial in the long run. ^{#programming #quizzes}

• Challenge your performance intuition with C++ operators Another interactive quiz where you get to estimate the performance difference between several variants of the same code. ^{#programming #quizzes}

• Fortran is still a thing A short essay about Fortran in the modern world. ^#programming

• Why Erlang is among the few true computer languages Usually, a language is something that is used for bilateral communication. For programming languages, this is often untrue. Erlang shows how this can be achieved still. ^#programming

• If I were to invent a programming language for the 21st century A short essay about the evolution of programming languages. ^#programming

• A cheap trick to speed up recursion in C++ More often than not, recursion is not your performance problem, to begin with. But even if it is, you can often avoid recursion altogether. When for some reason you can't, this trick helps. ^{#demos #programming}

• Polynomial approximation and interpolation This explains approximation and interpolation, how to use polynomials for that, and how to make both concepts work together. ^{#mathematics #tutorials}

• Interactive explanation of marching cubes and dual contouring Marching cubes and dual contouring are often used for mesh generation. This explanation shows how they work, what are their differences, similarities, and limitations. ^{#algorithms #mathematics #tutorials}

• Logic programming in C++ This shows that there is an invisible Prolog in every C++ compiler. It's up to you what to do with it but it's there. ^{#programming #tutorials}

• Tries as the evolution of nothing Trie is a data structure. Like “tree” but different. This tutorial explains the concept behind the trie, what makes it efficient, and when. ^{#algorithms #programming #tutorials}

• Programmer's guide to linear equations This is an introduction to linear equation systems. It explains linear dependency, under- and over-specification, direct and iterative solvers. The guide should give you enough knowledge to find a proper solution for your task but not enough to implement one efficiently yourself. ^{#mathematics #tutorials}

• Estimating floating-point error the easy way An explanation of how to measure computational error while working with floating-point numbers, and why. ^{#demos #mathematics #programming}

• APL deserves its renaissance too APL tutorial explaining the meaning of life←{↑1 ⍵∨.∧3 4=+/,¯1 0 1∘.⊖¯1 0 1∘.⌽⊂⍵} ^{#programming #tutorials}

• NURBS is just an acronym NURBS stands for the non-uniform rational basis spline. There are three separate concepts. This guide walks you through these concepts one by one. ^{#mathematics #tutorials}

• Playing a game of chance with C++ inline keyword It's about one particular aspect of C++ compilation that makes programming with the “inline” into a game of chance. ^#programming

• How much math can you do in 10 lines of Python An interactive introduction into concise Python / basic linear algebra. ^{#mathematics #programming}

• Outperforming everything with anything A 100 lines of Python code that substitute the compiler front-end for a specific computation. This shows that you don't need a “fast” compiling language to write efficient code. In fact, a compilation is only one of the multiple ways to achieve speed. ^{#demos #programming}

• Programmer's guide to polynomials and splines This is a brief introduction into polynomials. From how to make a polynomial run through your set of points to how to make it into a spline. ^{#mathematics #tutorials}

• Vastly outperforming LAPACK with C++ metaprogramming Still not really about LAPACK. It's a second part of the “outperforming” series explaining how the C++ metaprogramming can appear useful for efficient code generation. ^{#demos #programming}

• Outperforming LAPACK with C metaprogramming Ok, it's not really about LAPACK. You can consider it clickbait if you wish. It's about how to tell a compiler to write the code you want with a limited arsenal of tools the C language provides. ^{#demos #programming}

• Can you tell an assembly language when you see one? An interactive quiz featuring several obscure high-level languages and assembly variants. ^{#programming #quizzes}

• Mathematical analysis explained with Python, blood, and TNT A brief introduction to mathematical analysis with a little SymPy on the side. The page explains how to disassemble a function, and how to assemble it back from the derivatives. ^{#mathematics #tutorials}

• You don't have to learn assembly to read disassembly This is a very concise introduction to x86 disassembly. It shows that you probably have all the skills to start reading disassembly right now even if you thought it was too complicated for you. It really isn't, see it for yourself. ^{#programming #tutorials}

• An interactive introduction to iterative algorithms An interactive explanation of how iterative algorithms work. This explains convergence and the exit condition problem on an oversimplified linear system solver. ^{#algorithms #demos #mathematics}

• Challenge your performance intuition with C++ magic squares An interactive quiz where you get to estimate the performance difference between several variants of the same code. ^{#programming #quizzes}

• An interactive guide to homogeneous coordinates This interactive guide shows how homogeneous coordinates actually make geometry simpler and not more complicated. It explains the extra coordinate, the matrices, the generalized transformations. Most of what you need to know about projective geometry as a practicing programmer is here. ^{#mathematics #tutorials}

• So you think you know C? It's a C test. If you think you know C, take this test. It only has 5 questions. ^{#programming #quizzes}

• Learn you a Lisp in 0 minutes A short quiz to reveal your hidden knowledge of Lisp. ^{#programming #quizzes}

All the code is licensed under The Unlicense.