digits of pi in a spiral I wish to draw using Tikz a picture with the digits of pi in a spiral text  like this. Could you help?
Text spirals with TikZ I just ran across this, and I'm curious about whether it can be replicated in TeX...    Ideally one would have the spiral getting tighter and tighter as one got to the centre, as in    I know TikZ has the ability to fit text along a path, but I'm not sure how one might make text get smaller and smaller.  The closest I can find is , but that uses manually inserted font commands.  Edit: I got what I wanted using mwibrow's answer:
Classify orbits of conjugating action on $GL_2(\mathbb{C})$ Show that unit circle is not homeomorphic to the real line Can you choose which version of a game to play on Steam? How important are headings in SEO I heard the following dialog in a British English movie:     Words go round quick. All the little tongues go clack, clack, clack.   What does this mean, and why was the word "quick" used instead of "quickly"? Before Mavericks, I could use /etc/launchd.conf file to change maximum system resource consumption, for example:  limit maxfiles 16384 unlimited limit maxproc 16384 unlimited   It no longer works in Mavericks.  What is the correct way to do it in the recent version of OS X? How can I start automatically a command on Ubuntu 18.04? I am wanting to find the correlation between two variables: a categorical vegetation variable (with categories 1-4)  and a continuous variable of erosion (with values anywhere between 0.2 and 9). I think I would be required to use a non parametric test to find the correlation, but bit of a newby to stats so could anyone suggest the best test to use? I also wanted to know how sample size can affect these tests, ie with a sample size of 100 or 1000? Add table row in jQuery Difference between force.com and salesforce.com? What the difference between the two?  This description seems to be a bit out of date and underspecified. Printing a file to a printer in Ruby Finding a replacement for the scoreboard player test I am quite new to Javascript. I have made a html script that includes services I published to ArcGIS for server. It all does exactly what I want and I made it by copying working scripts together and getting help from more experienced scripters. I want to finetune my service by adding a legend. Unfortunately I am not able to create a working script. I have added the parts of my script I assume that are necessary to create my legend. Does anybody see what I am doing wrong?        &lt;script&gt;         var map;         var wmsLayer;         var URL;         var legend;         require(["dojo/query", "esri/map", "esri/layers/WMSLayer", "esri/dijit/Legend", "esri/config", "dojo/domReady!"],         function (query, Map, WMSLayer, Legend, esriConfig) {          esriConfig.defaults.io.proxyUrl = "/proxy/proxy_gcx.php";            map = new Map("map", {               basemap: "topo",               center: [5.5, 52.485],               minZoom: 8,               maxZoom: 13,               zoom: 8,               slider: true           });            wmsLayer = new WMSLayer("URL", {               format: "png",               visibleLayers: ["31", "30", "29", "28"]           });            map.on("layer-add", function (results) {               //add the legend               legend = new Legend({                   map: map,                   layerInfos: [{                       layer: results,                       title: "test"                   }]               }, "legendDiv");               legend.startup();           });             map.addLayer(wmsLayer);       });     &lt;/script&gt; &lt;/head&gt;  &lt;body&gt;     &lt;div id="map"&gt;     &lt;/div&gt;     &lt;div id="legendDiv"&gt;     &lt;/div&gt; &lt;/body&gt;   EDIT: I have edited the code. I am still not done. It does give me a legend on my browser but it says there is no content in there. On my arcgis server manager there is a legend. Why is Linux's filesystem designed as a single directory tree? Indenting a whole paragraph How do I indent a whole paragraph at the same distance from my left margin, with the simplest command or environment? Optimizing a "black box" function: Linear Regression or Bayesian Optimization... what's the difference? Goal: I have a function $f(x,y)=z$ (two variables for illustration only) which I know almost nothing about--it has a compact domain which I can determine, it is non-negative, and bounded above.  My goal is to find the maximum value $f(x,y)$ takes on its domain.  I can query the function and I know the values at a few points: $f(x_1, y_1)=z_1, f(x_2, y_2)=z_2,..., f(x_n, y_n)=z_n$.  Optimization via Linear Regression:  I have used linear regression (and related methods like the lasso) to model functions like this in the past; this is the method that I am very comfortable with.  Typically, I might try to find a polynomial (of degree $k$) which relatively accurately models the data. The end result would be to say that:   $$f(x,y)\approx \beta_1 + \beta_2 x + \beta_3 y + \beta_4 x^2 + \beta_5 xy + \beta_6 y^2 + ... + \beta_{m}y^{k}.$$  Determining the coefficients is done by solving the .  The "best degree" for the polynomial might be determined using $k$-fold cross validation.  Once the "best" polynomial has been determined, one can choose any of a number of methods to optimize it (Newton's method, gradient descent, hill climbing, etc).  Then, if all goes well, the optimal value on the polynomial corresponds to an optimal value of $f(x,y)$.  Bayesian Optimization:  Recently, I was describing this technique (linear regression) to a colleague who asked: "What is the difference between that and Bayesian Optimization?"  I've been attempting to answer this question for the last couple days, and so far I don't have anything really conclusive.  After reading , trying to read  and getting stuck reading  I think I understand the following about BO:   Start with a prior (a guess as to what family of functions the black box belongs to... or at least some family of functions which you believe might be able to describe $f$ well).  It looks using a  as a prior is popular. Specify whatever is needed to build your prior (for GP this is a covariance function). As you go along, you maintain two evolving functions, a "mean" function $m(x,y)$ and a "confidence interval" function $c(x,y)$.  Basically, you can predict the value at any point by evaluating $m(x,y)$ and you are confident that $f(x,y)\in [m(x,y)-c(x,y), m(x,y)+c(x,y)]$. Bayesian optimization provides a systematic way of updating/exploiting the model by alternatively selecting points where the confidence interval is wide (you are very uncertain about the value) or at optimal points on the model $m(x,y)$.   My Question: Is it fair/correct to say that the major difference between Bayesian Optimization and simply optimizing the linear regression model is that Bayesian Optimization provides the systematic way of sampling with the goal of optimizing the model and reducing uncertainty whereas the linear regression model ignores the idea of uncertainty and doesn't explicitly provide a means of updating the model?  Said another way, is the linear regression model an example of what might be a "mean" function $m(x,y)$ in Bayesian Optimization?  If I stick with linear regression, specify how to compute the uncertainty, and provide a means of updating/improving the model (exploit/explore) am I just doing Bayesian Optimization (without calling it that)?  Background: My background is in pure mathematics (graph theory) but my new job has me working with a lot of data (so I'm self learning statistics).  With that in mind, my statistics vocabulary is somewhat limited (so I appreciate answers that either avoid technical terminology or briefly explain any technical terminology used)--for example, Monday was the first time I heard/read the word "prior" used in a stats sense and I'm still not 100% sure I understand that correctly. Can't run "dpkg --add-architecture i386" on 12.04 64-bit to run eclipse ADT How to prepare/augment images for neural network? I would like to use a neural network for image classification.  I'll start with pre-trained CaffeNet and train it for my application.    How should I prepare the input images?  In this case, all the images are of the same object but with variations (think: quality control).  They are at somewhat different scales/resolutions/distances/lighting conditions (and in many cases I don't know the scale).  Also, in each image there is an area (known) around the object of interest that should be ignored by the network.  I could (for example) crop the center of each image, which is guaranteed to contain a portion of the object of interest and none of the ignored area; but that seems like it would throw away information, and also the results wouldn't be really the same scale (maybe 1.5x variation).  Dataset augmentation  I've heard of creating more training data by random crop/mirror/etc, is there a standard method for this?  Any results on how much improvement it produces to classifier accuracy? Usually in the morning I brush my teeth after breakfast. But my dentist told me that it's better not brush them right after eating food, because eating makes them soft.  So now I brush my teeth before breakfast. Is this the correct procedure?  PS. Just found , the author has the same opinion.  Just want to get a additional confirmation. Why do we use GLM?