In a previous post, I explained how to get a parameterization of a Hopf cylinder or torus. There is a clearer way, which I present here. For the Hopf map, the preimage of a point \(p... [Read more...]

I came across this interesting paper entitled Complex Variables Visualized and written by Thomas Ponweiser. In particular, I was intrigued by the generalized powers of a Möbi... [Read more...]

In this post, I show how to use the qTip2 JavaScript library to create some tooltips on the headers of a DT datatable in Shiny, displaying some information about the columns, such as summary stati... [Read more...]

In this post, I’ll show how to draw a stereographic duoprism using R, Asymptote and POV-Ray. With R library(rgl) A [Read more...]

The stereographic truncated tesseract Drawing with rgl (R) Drawing with Asymptote Drawing with POV-Ray The stereographic truncated tesseract ... [Read more...]

The shiny app Here is a simple shiny app: library(shiny) library(ggplot2) # UI #### ui [Read more...]

The five-parameters logistic curve is commonly defined by \[ f(x) = A + \frac{D-A}{\Bigl(1+\exp\bigl(B(C-x)\bigr)\Bigr)^S}. \] Assuming \(B__0\) and \(S__0\), ... [Read more...]

Preliminaries: the (scaled) Beta prime distribution Beta distribution of the third kind Update 2019-09-05: generalised Beta distribution ... [Read more...]

This is a Steiner chain with its enveloping cyclide: And these are nested Steiner chains: With R We will include the cyclides in the plot. We firstly write a functi... [Read more...]

Here is the code of this app: library(shiny) library(shinyBS) library(DT) library(ggplot2) ui [Read more...]

Edit cells on pressing Tab and arrow keys Select rows on click and drag Getting the selected rows Edit columns... [Read more...]

A. A. Ungar has developed the concept of gyrovector space. His theory provides a (gyro)vector approach to hyperbolic geometry. Ungar deeply studied three examples of gyrovector spaces; they ... [Read more...]

Let \(\iota_0\) be the inversion with respect to the unit circle: \[ \iota_0(z) = \frac{1}{\bar{z}}, \quad z \neq 0. \] Consider a generalized circle \(\mathcal{G}\mathcal{C}... [Read more...]

You are a R user and you have to evaluate the integral \[ \int_{-5}^4\int_{-5}^{3-x}\int_{-10}^{6-x-y} f(x,y,z) \,\mathrm{d}z\,\mathrm{d}y\,\mathrm{d}x \] for a certain function \(f\). How? ... [Read more...]