Creating a “Geometric Eye” Using Desmos

Geometric Eye

Several years ago, I came across some videos by the artist Dearing Wang that showed how to create mandalas and other geometric figures using only a compass and straightedge. One of them was a figure he called a “Geometric Eye“. Drawing one by hand took hours. Using the online Desmos math app, you can create one in minutes! Here’s my screencast explaining how:

Embedding Interactive Graphs in Haiku

I’m a big fan of the online graphing calculator at Desmos.com. My students and I use it all the time instead of graphing calculators because it is so much faster, and it is easier to enter functions. And now I just figured out that teachers who use Haiku can embed interactive graphs into their Haiku pages!

First, create a function with sliders. For example, in the function pane, enter y = m*x + b. Desmos will automatically ask you if you want to create sliders for m and b, so click “All”.

function

Next, copy the embed code Desmos provides by clicking on the “Share” button at the upper right (you have log into Desmos to access the Share feature).

Embed

Now go to the Haiku page where you want to embed the graph. Click “Add Content Block” and choose “Embed the Web”. Paste the code into the yellow box:

Haiku

Haiku will say it doesn’t recognize the code, but go ahead and click “OK”. Give it a title and place your content block where you wish, then hit “Save”. You should now see your Desmos graph in its own content block. When your students click on it, it will load a fully interactive grapher!

 

 

Getting Started With Haiku

A boon for teachers,

A space students can access;

Knowledge is shared.

Well, I’m not a very good poet, but I wanted to write a haiku in honor of the learning management system my school uses: Haiku. Other LMS’s include Moodle (which is open-source), and Blackboard. They all serve the same purpose: to provide teachers and students an online place where information can be shared. Teachers can post images, videos, assignments, worksheets, etc., and they can create forums for online discussions. Students can submit files to a “dropbox”, see a calendar that displays all of their assignments with due dates, and access all kinds of media posted by their teachers.

Harpeth Hall switched to Haiku this year, so I’m a newbie when it comes to utilizing all of its features, but I like it a lot. One of the best is the ability to rearrange content blocks by simply dragging and dropping them. Here’s what I’ve found works for me (so far).

I have created a separate page for every chapter we cover in a course. The page links are on the left, and the current one is always at the top. You can hide pages, so students don’t see them until you want them to.

Chapters

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In the middle pane, I post course content. In my case, that includes images, videos, and screencasts. It is extremely easy to embed YouTube videos – all you need is the URL, and Haiku does the rest.

Screencasts

In the top block, I like to post an image or short video that is relevant to that chapter’s material.

conics

In the right pane, I post links that are useful for the entire year, and the assignments for each chapter.

Assignments

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In the Welcome page, I post my Twitter feed; I’ve found that students really enjoy using Twitter with hashtags for various topics we cover.

Twitter

 

While this is just a bare bones explanation of what you can do with Haiku, I hope that seeing how I’ve organized it is helpful. At the beginning of the year, when I faced a completely blank site, it was rather daunting! Now that I’ve been using it for almost three quarters of a school year, I don’t know how I functioned without it. I’ve used Blackboard and Moodle, and without a doubt Haiku is the most flexible and user-friendly LMS available.

Creativity + Desmos = A Rewarding Math Project

A couple of weeks ago, I assigned a project to my Honors Precalculus students that made use of the fantastic online calculator, Desmos :

Honors Precalculus Desmos Project

In this project, you get to combine your mathematical knowledge with your artistic creativity.

Use the Desmos online graphing calculator (https://www.desmos.com/calculator) to plot a set of functions that create a picture. You must use at least 25 functions. You may use any type of function we’ve learned so far this year: polynomial, rational, piece-wise, trigonometric. You can add shading by using inequalities.

Save your finished project (include your name in the title), and submit it to me by using the “share graph” button on the top right:

 This project is worth 40 points.

Your masterpiece is due at the beginning of class Monday, November 25. We’ll view everyone’s submissions, and vote on the “Best in Show”. The winner will get a special prize!

The results far exceeded my expectations. The students threw themselves into the task with amazing enthusiasm. They learned all about restricting domains of functions, using inequalities for shading, and transformations. One student even researched how to rotate conic sections, and shared her new knowledge with her classmates.

If you are concerned about spending a lot of time learning a new program, fear not: Desmos is one of the easiest and most intuitive graphers I’ve ever worked with. They provide a brief but excellent user guide that can be downloaded here, as well as lots of video tutorials.

The gallery below contains all of my students’ final submissions, but I have to spotlight a couple students’ masterpieces. In the Beauty and the Beast one, the student used 406 equations to create it, and it is simply spectacular!

Newell

And here is a magnificent rendering of the Taj Mahal by another gifted mathematical artist:

Biegl

Here are the rest of their creations. Clicking on a thumbnail brings up the full-size image. Enjoy!

Update: Desmos featured one of my student’s work on Twitter!