Connecting Euclidean trigonometry and hyperbolic trigonometry.| Toby Lam’s Blog
Why does x = tan θ substitution work?| Toby Lam’s Blog
with 3d plots| Toby Lam’s Blog
without eigendecomposition| Toby Lam’s Blog
My watch has a “Noise” app: it shows , for decibels. My amp has a volume knob, which also shows decibels, although.. negative ones, this time. And finally, my video editing software has a ton of me...| fasterthanli.me
So I'm two months into trying to teach a proof of Fermat's Last Theorem to a computer. We already have one interesting story, which I felt was worth sharing. Continue reading →| Xena
The mathematician John Venn was born on this day in 1834. To commemorate the occasion, here’s a poem in the form of a Venn diagram.| Brian Bilston
I come back to my last experiment and explore whether the difference in gravimetric vs volumetric flow could be due to changing shot TDS.| Coffee ad Astra
What’s the action of a simple harmonic oscillator? And how does this change depending upon the path? Some mates of mine and I worked through this recently. This is my write-up of that calculation.| P.T.C.
If we are to believe the media we are bombarded with misinformation and disinformation - there's certainly a lot of it out there and Alex Edmans sets out to give a guide to the many ways that information can be badly or misleadingly presented, and how we can defend ourselves from it.At the heart of his argument are two biases. I'm so glad he limits it to two - I get totally lost trying to keep on top of all the biases that psychologists introduce, so sticking to confirmation bias plus black a...| Popular Science Books
Using band-edge filters for carrier frequency recovery with an FLL is an interesting technique that has been studied by fred harris and others. Usually this technique is presented for root-raised cosine waveforms, and in this post I will limit myself to this case. The intuitive idea of a band-edge FLL is to use two filters… Continue reading About FLLs with band-edge filters| Daniel Estévez
In a previous post, I proposed to study complex systems through a mereological lens by applying the Möbius inversion theorem. This has become my favourite theorem by now, because I think it allows you to do integration and differentiation on observables in complex systems where this was not possible before.| Abel Jansma
Learning through playing is the best way to learn! Use these mental Maths games to practice skills in a fun way!| Teach Me Mommy
I was looking for information about mathematics programs at other liberal arts colleges, so I put together this collection of links. I thought others might find it helpful, so I’m posting it here. (I actually asked ChatGPT to assemble this list. It did an OK, but not great, job. About 70% of the links were... Read More| David Richeson: Division by Zero
Networks are of huge significance to life and technology, so it was refreshing to read a popular maths title on the subject. I was a little ...| popsciencebooks.blogspot.com
Helen Neale posted on KiddyCharts How to help your kids with difficult subjects in school - check out our tips now to give you ideas on supporting your kids to succeed. The post How to help kids overcome difficult subjects in school appeared first on KiddyCharts.| KiddyCharts
One of the biggest developments in the history of maths was moving from describing relationships and functions with words to using symbols. ...| popsciencebooks.blogspot.com
A classic curate's egg of a book. Some aspects of it are brilliant, but there is enough that isn't to make it frustrating. Wisely, Oliver Jo...| popsciencebooks.blogspot.com
About a month ago I read this excellent piece of work https://blog.benjojo.co.uk/post/auditing-github-users-keys . My first reaction was kick myself for not thinking of it before. It reminded me of this paper https://factorable.net/paper.html and associated the presentation which is pretty special. One of the major tools used in that paper was use of a batch version of the Greatest Common Divisor algorithm that can efficiently find common factors in large numbers of semi primes. Common ...| Nat McHugh
Here is a little challenge I have had some fun with recently.| Nat McHugh
This thing got long and can basically be summarised as:| Nat McHugh
This seemed to be a book that had a lot going for it. The topic of 'the science of certainty' appealed to a reader like me who is fascinated...| popsciencebooks.blogspot.com
Today I wanted to talk about the scientific notes with (in my opinion) the funniest name ever: How Often Should You Beat Your Kids? by Don Zagier. Do not worry, it is not what it seems. Even though the paper states facts like the following:| Adri’s Blog
I love John Mason and although I’ve even quoted it myself a few times, I think I don’t wholeheartedly agree with the statement “it is the ways of thinking that are rich, not the task itself&#…| How I teach maths.
UPDATE: I have now found an explicit formula for the Möbius function on the redundancy lattice. This will appear in a preprint soon.| Abel Jansma
In my PhD thesis, I developed a method and software package to infer interactions and cell states from gene expression data. Both the software and the research are now published!| Abel Jansma
Generative models, in particular energy-based models, are often used to sample from conditional distributions–a process known as inpainting. One of the most fundamental kinds of generative energy-based models is called a restricted Boltzmann machine (RBM), which is essentially a bipartite, glassy Ising model. Inpainting with RBMs is usually done by sampling from the visible layer while fixing the value of some visible nodes, which is an intervention, not a passive observation. I could not f...| Abel Jansma
(This is an update on my Ethereum Protocol Fellowship. More updates can be found here ).| Abel Jansma
(This is an update on my Ethereum Protocol Fellowship. More updates can be found here ).| Abel Jansma
In today’s world, data is everywhere—and often, it’s overwhelming. Datasets can have hundreds or even thousands of features, many of which are redundant or noisy. Visualising data is an essential skill that allows Data Scientists to effectively highlight structures and relationships that would otherwise remain hidden. This series of tutorials will focus on Principal Component […] The post PCA for Programmers appeared first on Alan Zucconi.| Alan Zucconi
I mentioned in a previous post that doing exact UNORM or SNORM conversions to float in hardware was not particularly expensive, but didn’t go into detail how. Let’s rectify that! (If yo…| The ryg blog
For BC6H encoding in Oodle Texture, we needed a sensible error metric to use in the encoder core. BC6H is HDR which is more challenging than LDR data since we need to handle vast differences in magnitude. BC6H internally essentially treats the float16 bits as 16-bit integers (which is a semi-logarithmic mapping) and works with […]| The ryg blog
GPUs support UNORM formats that represent a number inside [0,1] as an 8-bit unsigned integer. In exact arithmetic, the conversion to a floating-point number is straightforward: take the integer and…| The ryg blog
The Triggernometry series mixes the grit of the west with a cast of mathematicians from across history to create a truly unique and unforgettable adventure. The second instalment – Advanced Triggernometry – finds Malago Browne riding out to defend a besieged town, along with six unlikely allies. Read on for an exclusive extract… Chapter One: … Continue reading Exclusive Extract: Advanced Triggernometry| STARK HOLBORN
The Godbolt Compiler Explorer is a fantastic tool for assembler programmers. In this post, I show you how to use Compiler Explorer to generate RISC-V assembly code and offer some ideas to make best use of this tool.| Project F
Integer multiply and divide instructions form the optional M extension. Making multiplication and division optional keeps the base instruction set simple and reduces the size of the smallest RISC-V core. This post includes a brief overview of common RISC-V extensions.| Project F
This RISC-V assembler post covers shift instructions, such as sll, srl, and srai. I also explain how to use shift instructions to quickly multiply and divide by powers of two.| Project F
This RISC-V assembler post covers bitwise logical instructions, such as and, not, and xori. Bitwise instructions carry out the specified operator on each bit of the sources in turn.| Project F
This FPGA demo uses fixed-point multiplication and a small framebuffer to render the Mandelbrot set. You can navigate around the complex plane using buttons on your dev board.| Project F
Welcome back to my series covering mathematics and algorithms with FPGAs. In this part, we dig into vectors and arrays, including slicing, configurable widths, for loops, and bit and byte ordering.| Project F
Welcome back to my series covering mathematics and algorithms with FPGAs. Project F is known for its practical, hands-on tutorials. So, I decided to dedicate a post to a topic usually ignored by FPGA authors: multiplication with DSPs.| Project F
Welcome to my ongoing series covering mathematics and algorithms with FPGAs. This series begins with the basics of Verilog numbers, then considers fixed-point, division, square roots and CORDIC before covering more complex algorithms, such as data compression.| Project F
In this how to, we’re going to look at a straightforward method for generating sine and cosine using a lookup table. There are more precise methods, but this one is fast and simple and will suffice for many applications.| Project F
The square root is useful in many circumstances, including statistics, graphics, and signal processing. In this how to, we’re going to look at a straightforward digit-by-digit square root algorithm for integer and fixed-point numbers. There are lower-latency methods, but this one is simple, using only subtraction and bit shifts.| Project F
In this FPGA demo we’ll experiment with Game of Life, a cellular automaton created by prolific mathematician John Conway in 1970.| Project F
Division is a fundamental arithmetic operation we take for granted. FPGAs include dedicated hardware to perform addition, subtraction, and multiplication and will infer the necessary logic. Division is different: we need to do it ourselves. This post looks at a straightforward division algorithm for positive integers before extending it to cover fixed-point numbers and signed numbers.| Project F
Sometimes you need more precision than integers can provide, but floating-point computation is not trivial (try reading IEEE 754). You could use a library or IP block, but simple fixed point maths can often get the job done with little effort. Furthermore, most FPGAs have dedicated DSP blocks that make multiplication and addition of integers fast; we can take advantage of that with a fixed-point approach.| Project F
This series will help you learn and understand 32-bit RISC-V instructions and programming. The first part looks at load immediate, addition, and subtraction. We’ll also cover sign extension and pseudoinstructions.| Project F
This is a result I must have re-derived at least 4 times by now in various ways, but this time I’m writing it down so I just have a link next time. All right. If you’re encoding a BCn o…| The ryg blog
some insight into arts place in the world relating to dyscalculia, so without any further ado here's the interview with Margot – The post Artist Margot Connop – Art & Dyscalculia appeared first on .|
My own mountain was always educational. Mathematical and numerical. My greatest supporters were always my parents. Some educational mountain climbers reach the top of the summit quicker than others. The ones who struggle are often left behind. And they cannot climb the mountain because there is no support for them. The post Accidental Mountain Climber By Mark Daly appeared first on .|
About a decade ago, a groundbreaking study found that eye pupils detect more than just light. But what has this got to do with dyscalculia? The post What Have Eyes Got To Do With Dyscalculia? appeared first on .|
It's the 1980s. I am sitting at a desk in primary school. It's senior infants. Although I was an easy-going kid, I would get frustrated that I could not do maths and got upset about that. There were five of us at the desk. The teacher is handing out copy books. we were doing maths work. She asked us who had finished the and they all put up their hands, and then she asked who had not finished the work, and I put up my hand. The teacher said that they would wait until Mark is finished. The pos...|
Roll up, roll up, roll up and welcome to the two hundred and twenty ninth Carnival of Mathematics! 229 is a prime number, and that in itself is interesting. Its the “elder” of a set of …| cavmaths
There's no doubt that Matt Parker can make practically anything interesting - this is one of the few books I've ever read where I genuinely ...| popsciencebooks.blogspot.com
Popular mathematics can be hard to make engaging. Though some topics (such as infinity or zero) can be made interesting in isolation, usuall...| popsciencebooks.blogspot.com
We will see that the 3D plot of \(x^2 + (y+zi)^2 = 1\) contains a circle and a hyperbola, where \(i\) is the imaginary number. Beyond the visuals, this helps us understand the (complex) eigenvalues of real matrices.| Toby Lam’s Blog
Given some f(x), what’s the taylor series of f(x)^p for some real p?| Toby Lam’s Blog
By introducing some notation on the image and pre-image function, one could derive more elegant definitions of continuity, subspace topology and quotient topology. This notation is not new.| Toby Lam’s Blog
Many moons ago, Vsauce tweeted:| Demian’s blog
The Parks-McClellan FIR filter design algorithm is used to design optimal FIR filters according to a minimax criterion: it tries to find the FIR filter with a given number of coefficients whose frequency response minimizes the maximum weighted error with respect to a desired response over a finite set of closed sub-intervals of the frequency domain. It is based on the Remez exchange algorithm, which is an algorithm to find uniform approximations by polynomials using the equioscillation theor...| Daniel Estévez
While teaching non-right angled trig recently it occurred to me that when doing the questions myself, I don’t actually thing about the formula all that much. Particularly with the sine rule. Yet I still start the teaching of it using the formula heavily. It made me wonder if this was really all that necessary. Firstly […]| cavmaths
Over the weekend I happened accross this loevely puzzle on twitter. It was tweeted out by Diego Rattaggi (@diegorattaggi) and I saved it to my ever growing folder of puzzles to try on my phone. When i had a bit of time spare I thought I would give it a go. Have you had a […]| cavmaths
Recently I gave some of my year 12 students some practice papers as homework to aid their revision. When they brought them back in one of them had literally copied to entire markscheme into to the answer paper, while another had watched a walk through and written up the answers with notes on how to do it next […]| cavmaths
Came across another nice puzzle from Mr Gordon (@MrGordonMaths): First thing I noticed was that it was a pythagorean triple. My initial thought was that there might be a solution involving circle theorems, but then I realised that as an area was given this might be the best route. As angle QPS IS 90, then […]| cavmaths
Earlier today I was discussing and thinking about football accumulators, and accumulators in general. In case you don’t know what one is here is a quick overview. You basically pick a set number of bets and put an initial stake on, then if your first bet wins the winnings and stake roll over to the […]| cavmaths
I’ve been looking through my saved puzzles again and I found this nice little one in the maths newsletter from Chris Smith (@aap03102): It’s a nice little question that took me some thinking about. First I considered the half squares with hypotenuse 2. As these are isoceles RATs, that means their side length is rt2 […]| cavmaths
Today I want to look at another puzzle I found on math walks (from Traci Jackson @traciteacher): I love these 1-9 puzzles, and thought I’d have have a crack. First I considered the 9, with the 1 gone already that means that the 9 must share a line with the 2 and the 3 to […]| cavmaths
Coefficients of a product of polynomials can be generated by a multiplication between a matrix and a vector.| Toby Lam’s Blog
This article will explain how to create four dimensional objects, in a format compatible with the Unity4D extension. You can find all the articles in this series here: Introduction The past three articles in this series talked at length about hypercubes and hyperspheres. And while Part 1 gave some basic intuitions on how hyperobjects are […] The post Unity 4D #4: Creating 4D Objects appeared first on Alan Zucconi.| Alan Zucconi
This article will explain how to render 4D objects in Unity, using three separate technique: orthographic projection, perspective projection and cross-section. You can find all the articles in this series here: A link to download the Unity4D package can be found at the end of this article. Introduction It is undeniable that what makes hyperdimensional […] The post Unity 4D #3: Rendering 4D Objects appeared first on Alan Zucconi.| Alan Zucconi
This article will show how to extend Unity to support four-dimensional geometry. This is the second article in a series of four, and the first one which will probably start discussing the Mathematics and the C# code necessary to store and manipulate 4D objects in Unity. You can find all the articles in this series […] The post Unity 4D #2: Extending Unity to 4D appeared first on Alan Zucconi.| Alan Zucconi
This is the first part of a series of articles dedicated to extending Unity from 3D to 4D. In this instalment, we will explore the fourth dimension, from its representations in movies and video games, to its more mathematical and geometrical interpretations. At the end of the series, you will learn how to create and […] The post Unity 4D #1: Understanding the Fourth Dimension appeared first on Alan Zucconi.| Alan Zucconi
This post continues our journey through the Mathematical foundations of iridescence. This time, we will discuss a new way in which material can split light: thin-film interference. This is how bubbles (and car paint) get their unique reflections. You can find the complete series here: Part 1. The Nature of Light Part 2. Improving the […] The post The Mathematics of Thin-Film Interference appeared first on Alan Zucconi.| Alan Zucconi
This is the third part of the series dedicated to one of the most popular sensor de-noising technique: Kalman filters. This article will explain how to model non-linear processes to improve the filter performance, something known as the Extended Kalman Filter. You can read all the tutorials in this online course here: Part 1. A […] The post The Extended Kalman Filter appeared first on Alan Zucconi.| Alan Zucconi
This is the third part of the series dedicated to one of the most popular sensor de-noising technique: Kalman filters. This article will explain how to model processes to improve the filter performance. You can read all the tutorials in this online course here: Part 1. A Gentle Introduction to the Kalman Filter Part 2. […] The post Modelling Kalman Filters appeared first on Alan Zucconi.| Alan Zucconi
This is the second part of the series dedicated to one of the most popular sensor de-noising technique: Kalman filters. This article will introduce the Mathematics of the Kalman Filter, with a special attention to a quantity that makes it all possible: the Kalman gain. You can read all the articles in this online course […] The post The Mathematics of the Kalman Filter appeared first on Alan Zucconi.| Alan Zucconi
Στις 08/05/2015 στην βουλή σχολιάστηκαν οι ηλεκτρονικές ψηφοφορίες των πρυτανικών συμβουλίων και ουσιαστικά ο Πρωθυπουργός κ. Τσίπρας υπερασπίστηκε την κατάργησή τους. Το κύριο πρόβλημα (μου) με το παραπάνω είναι οι λόγοι που ισχυρίστηκε η κυβέρνηση πως προχωρά σε κάτι τέτοι...| Into.the.Void.
An IIR filter deconvolving a blurred 2D image in four “recurrent” sequential passes. This post is a follow-up to my post on deconvolution/deblurring of the images. In my previous blog p…| Bart Wronski
This post covers a topic slightly different from my usual ones and something I haven’t written much about before – applied elements of probability theory. We will discuss what happens with “n…| Bart Wronski
Connecting metrics with refractive indexes| Toby Lam’s Blog
On maths I find interesting and my life| Toby Lam’s Blog
Curvature is analgous to centripetal acceleration| Toby Lam’s Blog
Centroid Spherical Polygon| skeptric.com