1. Introduction

I’m a person who likes to try new things, and I recently found a fun and useful mathematical drawing website. Can be used for numerical calculation, function drawing (dynamic function support), geometric drawing and so on. In mathematical modeling, paper function drawing, dynamic display function changes and so on May be used. So, let me introduce you to this website.

2. Introduction to usage

The first, of course, is to post its official website: www.desmos.com/

Click Start Graphing to get started, and the blue buttons below are some of its sub-functions, so don’t pay too much attention.

2.1 Main Screen Function Description

Focus on the white space on the left, as this is where most of the rest of the action will be done. In addition, the Share button can be used to download the images you have drawn, and the Question mark button has an introductory tutorial (the video tutorials are on YouTube, so you may need to go to science).

Click on the sidebar to see that the site gives us many templates, we can click on any one to see the effect, here I open a fourth order polynomial fit:

On the left is the core of the entire drawing.

First, input the x and y coordinates of the scatter point, and then input the expression to be fitted in the second column. In Desmos, ~ stands for regression fitting, and the fitting parameters are A, B, C, D and F. Once the input is complete, it will automatically merge the drawing image and then display the parameters.

2.2 Basic Functions

2.2.1 Basic function drawing and calculation

Create a new drawing board. Enter in the first column. The following figure can be obtained:

How do you get the value of the function at a certain point? There are three ways:

  • Mouse click graphics, this is the simplest, but also the most inaccurate.

  • Get from subfield input:

  • Convert to table, click the Settings button in the Coordinates panel, and click Convert to Table. The following figure is obtained:

It can be inserted anywhere in the X-axisxIt will give you the result automatically. If I want to knowWhat is equal to.

Alternatively, you can add columns (add other functions) to get different values for the same x value:

In addition to obtaining different values of the function, the scatter diagram of the increased function is also obtained. How do I modify the drawing style? Long pressThe green icon on the left gives you the image below:

Here you can modify the style and color, the specific effect can be their own try, I will add the line here.

As an added bonus, the set of functions supported by the site can be viewed below:

2.2.2 folder

When drawing multiple graphs, we need a way to manage multiple graphs. Fortunately, Desmos provides folder management, which allows you to hide/show multiple functions in one click. The usage is as follows:

  1. Click the + sign in the upper left corner to create a new folder
  2. Write arbitrary expressions and drag and drop them into folders.
  3. Click the icon of folder coordinates to realize multiple graphics hidden and displayed at the same time

2.2.3 list

In Desmos, lists can be defined to express multiple figures as follows:

A = [1, 2, 3]

You can also define it by step size

A = [1…10] The default step is 1

Or a=[0,5…100] deduces a step size of 5

It can then be used like the following:

Or you can draw multiple points at the same time:

2.2.4 Sliding Variable (Slider)

Sliding variables can be defined in Desmos to draw dynamic images.

Defining a sliding variable is easy, just remember one rule: don’t use common mathematical symbols,x,y, T,r, etc. Then write the expression desmos will automatically prompt you whether to generate sliding variables. Such as:

By sliding the slider or clicking Play, a motion picture will be drawn in the drawing area on the right. (Hint: there is a speed control slider on the right side after clicking play).

Here is an advanced one:

Doesn’t it feel funny?

2.2.5 Parametric equations and polar coordinates

Desmos also supports parametric equations. For example, we use parametric equations to draw a circle:

Let’s look at polar coordinates

indesmosIn, polar coordinates are marked by the symbols R andIt means, draw a four-leaf clover.

Pretty simple.

2.2.6 inequality

So before WE get into the inequality, let’s talk about how you can restrict your domain or your range in Desmos. You do this by adding constraints between braces {}. As follows:

OK, so with that in mind, let’s look at how we can use inequality. Suppose I wanted to draw a graph that looks like this:


So I’ll draw it like this.

(PS: When I was in high school, there was a class of maxima and minima that needed to be drawn.)

2.2.7 integral

Desmos supports integral calculation as well as variable upper (lower) limit functions. Automatically add integral symbols by typing int, as in:

3. The conclusion

Well, that’s enough for the basics of Desmos, but there are many more advanced uses available in the templates and documentation, as well as the official Desmos tutorial. I think it is fun to learn, I hope to help you.