mbarnett16

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0 years, 301 days
Current undergraduate student at the University of Waterloo studying mathematics. Maplesoft co-op student working as a content developer.

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These are Posts that have been published by mbarnett16

The Lunar New Year is approaching and 2024 is the Year of the Dragon! This inspired me to create a visualization approximating the dragon curve in Maple Learn, using Maple. 

The dragon curve, first described by physicist John Heighway, is a fractal that can be constructed by starting with a single edge and then continually performing the following iteration process:  

Starting at one endpoint of the curve, traverse the curve and build right triangles on alternating sides of each edge on the curve. Then, remove all the original edges to obtain the next iteration. 

visual of dragon curve iteration procedure 

This process continues indefinitely, so while we can’t draw the fractal perfectly, we can approximate it using a Lindenmayer system. In fact, Maple can do all the heavy lifting with the tools found in the Fractals package, which includes the LSystem subpackage to build your own Lindenmayer systems. The subpackage also contains different examples of fractals, including the dragon curve. Check out the Maple help pages here: 

Overview of the Fractals Package  

Overview of the Fractals:-LSystem Subpackage 

Using this subpackage, I created a Maple script (link) to generate a Maple Learn document (link) to visualize the earlier iterations of the approximated dragon curve. Here’s what iteration 11 looks like: 

eleventh iteration of dragon curve approximation  

You can also add copies of the dragon curve, displayed at different initial angles, to visualize how they can fit together. Here are four copies of the 13th iteration: 

four copies of the thirteenth iteration of the dragon curve approximation 

 

Mathematics is full of beauty and fractals are no exception. Check out the LSystemExamples subpackage to see many more examples. 

 

Happy Lunar New Year! 

 

Can’t seem to find the mistake in your math? Instead of painfully combing through each line, let the new “Check my work” operation in Maple Learn help! Now in Maple Learn, you can type out a solution to a variety of math problems, and let Maple Learn check your work! Additionally, by signing on to Maple Learn and the Maple Calculator app, you can take a photo of your handwritten math, import it into Maple Learn, and check your work with the click of a button.

Whether you’re solving a system of linear equations or an algebra problem, computing an integral or a partial derivative, “Check my work” can help. Maple Learn will tell you which steps are “Ok” and which steps to double-check. If you get a step wrong, Maple Learn will point out which line has an error, then proceed to check whether the rest of your work followed the right procedure.

Here’s an example of a solution to a system of linear equations written out by hand. All I had to do was snap a picture in the Maple Calculator app, and Maple Learn instantly had my equation set ready to go in the Cloud Expressions menu. Then, I just clicked “Check my work” in the Context Panel.

Screenshot of a handwritten solution to a system with three linear equations and a screenshot of how the expressions appear in Maple Learn through the Cloud Expressions feature.

Maple Learn identified that I was trying to solve a system with 3 equations, checked my steps, and concluded my solution set was correct.

Screenshot of the feedback "Check my work" gives to the steps that correctly solve a system of three linear equations. "Ok" for correct steps, and a concluding message once completed.

What happens if you make a mistake? Here’s an example of evaluating an improper integral with a u-substitution that involves a limit. This time, I directly typed my steps into Maple Learn and pressed “Check my work” in the Context Panel. Check my work recognized the substitution step and noted what step was incorrect; can’t forget to change the limits of integration! After pointing out where my mistake was, Maple Learn continued to evaluate the rest of my steps while taking my error into account. It confirmed that the rest of the process was correct, even though the answer wasn’t.

Screenshot of incorrect steps in Maple Learn attempting to solve an improper integral. The error is highlighted with the feedback of "Check this step" from "Check my work"

After making my change in Maple Learn and checking again, I’ve found the correct value.

Screenshot of the corrected steps to solving the improper integral, with the positive feedback from Check my work indicating these steps are correct.

Checking your work has never been easier with Maple Learn. Whether you want to type your solution directly in Maple Learn or import math with Maple Calculator, the new “Check my work” feature has you covered. Visit the how-to document for more examples using this new feature and let us know what you think!

 

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