Week 5

Last Week's Problems - Video Solutions

Venn Diagram Solution

Perpendicular Gradients Solutions

Curve Stitching

This week is half term so we thought you might like to have some fun with straight lines making Art.

Curve stitching is the art of creating 'curves' using only straight lines. This was traditionally done with pins, string and a lot of time. With the help of Desmos, and a bit of maths, we can create amazing patterns quickly.

If you want to see how one of the examples was created click the picture to open the graph in Desmos, but it would be great if you could create it yourself.

I would love to see what you have done... email me at wokcolmaths@gmail.com

Getting started

Open Desmos and start typing in some equations of straight lines on the right hand side; it should be pretty intuitive.

Now, using what you know about straight lines, see if you can make this picture.

Generalising

Did you notice a pattern in your equations? If you would prefer to type less (mathematicians hate typing!) try using Desmos' “free variables”. If you type the equation “y=mx +c” you will be asked to “create sliders” for your free variables m and c. This allows you to easily explore how m and c affect how your straight line looks.

Instead of a slider you can create a list of values in Desmos. This lets you generalise your equations, and make use of the patterns you have spotted. For example I can create three parallel lines using the free variable ‘c’.

See if you can create your original pattern using only one equation. There is more than one way to do this. If you need a bit of a hint, have a look at one solution here: https://www.desmos.com/calculator/2mvw4km4vt

Extending

Now, wouldn’t it be nice to have more than 6 lines? Look at your equation and see if you can turn “6” into a free variable. That way you can have as many lines as you like….. now that has saved a LOT of typing. If you need a hint, there is one solution here:

Neatening

In Desmos you can display part lines by restricting the x or y values that you want. After your equation you can type the values you want using an inequality in curly brackets e.g. { 0 < x < 5}. You can use this to make your graphs look neater. Example here.

Challenges

There’s no limit to the number of patterns you can make!

Try extending your pattern to all 4 quadrants

(I couldn’t think of a way to do it with fewer than 4 equations – maybe you can?)

Can you make a "circle"?

Hint: The easiest way to do this is to think about transformations.

How do you shift a function vertically? Horizontally?

(Actually this is not quite a circle – if you can prove that then you are really flying!)

Use inequalities to shade the graph

007?

There are a lot of things you can draw with curves, but what can you draw with just straight lines?

We would love to see what you create, please send us your graphs at wokcolmaths@gmail.com

For some inspiration see below:

Finally, Harriet made the Woking College W fly around! Link here. I think it's fairly spectacular!

What can you do with animation?

This Week's Test and Last Week's Solutions

Last Week's Test Solutions

This Week's Test

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