Lesson video

Hi, I'm Mrs. Wheelhouse, and welcome to today's lesson, which is from the unit Maths in the Workplace.

In this series of lessons, we're exploring how maths is used in different careers.

Let's get started.

In today's lesson, you are gonna learn some of the ways that maths is used by graphic designers.

Now, what is a graphic designer? Well, a graphic designer creates visuals for various projects, such as adverts, branding, magazines, packaging and websites, and we're gonna look at some of this today.

Our lesson is broken into two parts, and in the first part, we're gonna consider something called the golden ratio.

A graphic designer creates visuals for various projects, such as adverts, branding, magazines, packaging and websites.

Here are some logos now, and you may recognise some of these.

These are all logos that have been created by graphic designers.

That's an interesting question, Andeep.

How has maths been used to generate those images? Well, Alex points out that, "Part of the design work involved some maths referred to as the golden ratio." But what is that? Now the word ratio might be familiar to you.

It might be something that you've used quite a bit in maths.

What's this golden ratio about? Well, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

For example, if we have two quantities, A and B, then A and B are in the golden ratio, if A to B is the same as B to A plus B.

Now we can express this in a different way.

We can say that B divided by A is equal to A plus B divided by B, and that should give us a value of approximately 1.

618.

That's a great question, Andeep, because so far I've seen that if two quantities have this particular relationship, they're said to be in the golden ratio.

But how is that actually useful? "Hmm, says Alex, "let's maybe consider something more visual," and that would make sense, we are looking at graphic design after all.

So here I've got a grid.

The two coloured squares are the same size.

The next square has a length which is approximately 1.

618 times the length of a small coloured square, again, only approximately.

Now we continue this pattern and the next square has a length, which is approximately 1.

618 times the length of the previous square.

Now, by drawing within the squares, images can be created that are within this ratio.

So let's see how I could use these shapes.

Well, I can create patterns with them, such as this.

Now, this is a very quickly put together image.

Graphic designers can produce far more complex images using building blocks like this.

So they could, for example, have arranged these triangles in a different way.

So quick check, a graphic designer creates visuals for various projects, such as adverts, branding magazines, packaging and websites.

Is that true or is that false? Pause the video while you make your choice now.

Welcome back.

You should, of course, have picked true.

Graphic designers work on various projects, and maths can aid them in designing images that will appeal to the public.

It is time now for your first task.

For question one, I'd like you to design a logo for a company using the golden ratio template, and then write a paragraph detailing why your logo represents the company well.

For example, if you chose a restaurant chain and you designed a burger, then this logo is in keeping with what the restaurant chain stands for.

Here is your template.

So what I'd like you to do now, please, is pause the video while you work on your design.

Welcome back.

I hope you had fun doing your design.

What I'm going to do now is share with you an example of what you might have done.

So for example, using the template, I placed circles in each smaller section, and you can see them there.

So I then used copies of these to design my logo.

So I started with the largest of the circles, and then I chose two of the smallest ones, not the smallest, but only one size up.

And then I chose to use the circle that's a little bit bigger than the ones I used previously, but you can see that I've only used part of it 'cause I partially hid them behind the larger circle.

Have you worked out what it is I'm drawing yet? No? All right, let's keep going.

So I did the second largest circle on the top, a couple more, I think you may have guessed what I'm drawing now.

I took the two smallest circles, coloured them in and used them here, and then I used an arc of one of the circles to create the mouth.

So I've designed a logo for a company that sells products aimed at toddlers.

Now the teddy is made from circles, which means the teddy has a soft round appearance, it looks cuddly and it looks safe for children.

Remember, I don't only want to appeal to toddlers, I want to appeal to their parents too, so that they might think this is a good place to buy toys for their children.

I hope you had fun doing your designs.

What you might like to do if you are in a class is consider presenting on your designs to each other so that you can share what you've all been up to.

It's now time for the second part of our lesson, which is looking at rotational symmetry in art.

Now, the golden ratio is not the only bit of math that graphic designers can use to help create images.

Rotational symmetry can also help.

Islamic designs are sometimes created from the repeated use of basic shapes.

They can create beautiful complex designs as a result.

And here's an example.

What shapes can you see in this design? Pause the video now while you have a chat with the person next to you or have a think for yourself.

Welcome back.

I suspect you all easily picked up on the hexagon, but did you pick up on the other shapes? Celtic designs, such as this version of the Celtic Knot, also rely on rotational symmetry.

A quick check now.

True or false, only Western cultures use geometric shapes in their designs? Don't forget, you need to justify your answer too, so pause the video now while you make your choice.

Welcome back.

What did you go for? Well, you should have said it's false.

Many different cultures create patterns using geometric shapes, and you could in fact pause the video now to go and research other cultures that also do this.

Now, Andeep has an interesting question here.

He wants to know if it matters whether there's rotational symmetry or not.

So Alex has a great idea.

We're gonna, "Consider two designs made entirely from triangles." We'll look at one design with rotational symmetry and one without.

This is our design with rotational symmetry.

Now, you might want to pause at this point and just reflect on, does the shape appeal? Does it look nice? Does it not look nice? What do you think about it? Right, now you've got some initial ideas, let's look at one made with triangles that has no rotational symmetry.

Oh my.

I don't know about you, but that to me looks quite messy.

I know which one I prefer, but what about you? Pause the video and have a quick chat to decide which one you prefer and why.

Welcome back.

I suspect you've picked the one with rotational symmetry, and that's because our brains are hardwired to like patterns.

The patterns are pleasing to us, and when we see something that's a bit disjointed, such as the shape that you can see on the right, it's not as appealing to us.

It's now time for your final task.

For question one, part A, I'd like you to create a design using basic shapes.

Your design should have rotational symmetry.

And then, in part B, create a second version of your design that does not have rotational symmetry.

Pause the video and do this now.

Welcome back.

For question two, I'd like you to show your two designs to your classmates, your friends or your family, and ask them, which image appeals more to you? Record the results.

Now it's up to you how you record these results.

If you've got a lot of people, you might want to consider a tally chart as opposed to just writing down which design is more appealing.

But it's up to you.

Another question three, I'd like you to create a chart to display your results.

Which image is more popular and why do you think this is? Now, it's up to you what kind of chart you do, you could do a bar chart, pie chart, completely up to you, but make sure that you have some form of key or way of identifying which graphic belongs to which design, i.

e.

if it's a bar chart, which bar belongs to which design? And if it's a pie chart, which area belongs to which design? Pause the video while you do this now.

Welcome back.

So what we're gonna do now is I'm gonna go through an example of what I came up with and you can compare it to what you've done.

So the first thing I had to do was create a design using basic shapes, and my design needed rotational symmetry.

And then, in part B, I had to create a second version that did not have rotational symmetry.

Well, in classic fashion, I'm going to say, "Here's what I made earlier." You might recognise these because I showed this design earlier on in the lesson, so I'm gonna use this.

After all, I did design it.

And then, question two, I went out and asked people which of the designs they preferred and I recorded the results.

Now, I used a very basic tally chart for this, and here they are.

So you can see that Design 1 was preferred by 14 people, and Design 2 was preferred by six people.

Now I opted for a tally chart 'cause I thought this was quite an easy way for me to count the results, but again, you might have gone for something different and it's absolutely fine if you did.

I can also easily see that I asked a total of 20 people.

So question three, I had to create a chart.

Now I went for a bar chart, and you can see there were 14 people that liked Design 1, and six people that liked Design 2.

Now again, you might have gone for a pie chart, absolutely fine if you did.

Given I had 20 people, a pie chart would've looked quite nice.

But I've opted for a bar chart.

So which one was more popular? Well, for my particular case, it was Design 1, and I had to say why I thought this was.

Well, I've said, "I think this is because the first design made a repeating pattern, and this is more appealing than the jumbled mess of the second design." You might have even used the phrase aesthetically pleasing.

Now, if you're not sure what that phrase means, do feel free to pause the video and go and look it up.

Aesthetically pleasing, quite a nice phrase to use, and I think it sums up very well Design 1 and does not represent Design 2 at all.

But what did you notice when you did your results? Did you see the same as me? Or was your design with no rotational symmetry more popular? if you're in class, might be worth seeing what everyone's results were.

Was Design 1 always the most popular or did sometimes Design 2 win? It's time to sum up what we've looked at in today's lesson, a graphic designer creates visuals for various projects, such as adverts, branding, magazines, packaging and websites.

Images that have rotational symmetry are often very appealing.

Do you remember the phrase we used? That's right, aesthetically pleasing.

I really hope you've enjoyed today's lesson and seen ways that math can be used by very creative people to produce beautiful designs.

You may want to go and look further into this, and if you type into a search engine anything such as golden ratio with designs or logos, you'll get to see even more examples of how maths is used to produce beautiful images.

Well done, you've done a great job today.

I look forward to seeing you next time for some more maths.

Goodbye for now.