Falling Ladder via Desmos

by DesignMakeTeach Feb 27, 2016
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I'm a bit puzzled about this graph because it doesnt look like the envelope of a falling ladder - whose endpoints I think are defined by

[x,0], [0,sqrt(l ^ 2 - x ^ 2]

but in this graph the endpoints here are equally spaced in both x and y axes ie.
[x,0],[0,l - x]

This thing is a 3D rendering of a 2D graph example in Desmos.com that is named Lists: Falling Ladder https://www.desmos.com/calculator/xdpigkjalg The purpose is to provide a model demonstrating the end product of the conversion of 2D graph in Desmos to a 3D model. It appears that the file name of the example was meant to be descriptive of the type of graph. Looking at the classic Falling Ladder problem, this would a great example of an incorrect solution to the problem. If you wanted to graph an example of a better solution in Desmos.com, I would be glad to convert it and add to this model or link to a better solution if you want to post one. Thanks for taking a look.

That's quite a long tool chain. It might be interesting to compare the use of OpenSCAD for simple cases like this to generate the STL directly:

module line(x,y,thickness=1) {
    hull() {
        translate([0,y]) circle(d=thickness);
        translate([x,0]) circle(d=thickness);

length = 100;
   for(x = [0:length/10:length]) {
      y = sqrt(length * length - x*x);
 //   y = length-x;  for the example curve
      echo(x,y,sqrt(x*x + y*y));

Audience is K12 math educators that are new to idea of 3D printing. Many of them already have heard of or use Desmos.com so this thing is for that specific workflow.
Tool chain boils down to: Convert image to SVG --> Import to Tinkercad

For OpenSCAD toolchain I am going to suggest https://blockscad.einsteinsworkshop.com/ as it is a nice transition from Scratch and Hour of Code style programming to OpenSCAD modeling.

BlocksCAD is what I've been using with my 9-10 year olds at Code Club here in Bristol. I've some worksheets which may be some use to you with some modules and projects - including one for the falling ladder graph I've just put up - and printed! Thanks for the suggestion - I might try it with my kids - who are at the moment making model furniture!


I think BlocksCAD is a great language to use after Scratch and the kids love getting something tangible to take home.