Lists

By defining a list of values, you can quickly plot a series of points, lines, or curves, or calculate statistical values such as mean, median, or standard deviation. Get started with the video on the right, then dive deeper with the resources and challenges below.

Create a list of values in between square brackets and separate elements with commas, such as \([1,3,4]\).

To generate a list of evenly spaced numbers, use an ellipsis. For example, \([1...10]\) represents the list of integers between \(1\) and \(10\) and \([1,3...11]\) represents the list of odd integers between \(1\) and \(11\).

You can use lists in any expression where you would use a single number, including the definition of a variable. This allows you to graph multiple lines or curves simultaneously.

If \(L\) is a list, you can refer to individual elements or subsets of elements by choosing the index of that element:

• Access the first element of \(L\) with \(L[1]\)
• Create a new list of the first, third, and fifth elements of \(L\) with \(L[1,3,5]\)
• \(L[1…5]\) accesses the first \(5\) elements
• Generate a list of elements of \(L\) from the third to the last with \(L[3…]\)
• Pull out the positive elements of \(L\) with \(L[L \gt 0]\)
• If \(M\) is another list, produce a list of elements from \(L\) at the indices specified by \(M\) with \(L[M]\)

See examples of each of these here.

In Desmos Geometry, use lists to define parameters in transformations, create concentric circles, or make “string” art with gliders. Read more about gliders in our Sliders and Movable Points article.

In Desmos 3D, you can use lists to plot multiple points and graph multiple curves or surfaces. For instance, if you define a list \(L=[-4…4]\), then the expression \((L,L,L)\) will graph \(9\) points arranged in a diagonal line. Similarly, the expression \((L\sin(t), L\cos(t), L)\) will graph \(9\) circles, each with a radius and position on the \(z\)-axis defined by the values of \(L\).