# Math question :o

Discussion in 'Community Discussion' started by lamina, Sep 2, 2010.

1. ### lamina macrumors 68000

Joined:
Mar 9, 2006
Location:
Niagara
#1
Hey guys,

I've been getting into Illustrator lately and I want to make a graphic of the iPod touch/iPhone screen, and illustrate the size of the iPod nano's screen against that of the iPod touch/iPhone.

That involves math.

The iPhone's screen measures 7.6cm tall by 5.1cm wide.

So I make a box that is 7.6cm by 5.1cm.

However, I only know the diagonal measurement of the new nano. It is 1.54in (3.9116cm).

How can I find out the size of the iPod nano screen, based only on two facts:

1) The screen is perfectly square (or appears to be)
2) It measures 3.9116cm diagonally

Joined:
Jul 24, 2010

Joined:
Jul 24, 2010
4. ### Nugget macrumors 68000

Joined:
Nov 24, 2002
Location:
Houston Texas USA
#4
You managed to misspell every word in your post.

Here's what we know from apple.com:
• 1.54-inch (diagonal) color TFT display
• 240-by-240-pixel resolution
• 220 pixels per inch

From this we can infer that a^2 + b^2 = 1.54^2. Since it's square, we also know that a==b. Solving for a/b...

That gives us 1.0889" per side (roughly)

5. ### lbro macrumors 6502a

Joined:
Jan 22, 2009
#5
a2+b2=c2

a=2.7659188 cm (or, 1.0889444")
Derived via pythagorean theorem.

6. ### SilentPanda Moderator emeritus

Joined:
Oct 8, 2002
Location:
The Bamboo Forest
#6
I believe it's 1.1" by 1.1". or 2.794cm

This is based on:

1.54-inch (diagonal) color TFT display
240-by-240-pixel resolution
220 pixels per inch

That means it's 240 pixels on each side and is square.

220 pixels = 1 inch

20 more pixels is .090909 and some change

7. ### Nugget macrumors 68000

Joined:
Nov 24, 2002
Location:
Houston Texas USA
#7
Awesome. Two approaches (math and measurement) and we agree to within 0.001"

I'd say that's conclusive.

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Mar 9, 2006
Location:
Niagara
9. ### lamina thread starter macrumors 68000

Joined:
Mar 9, 2006
Location:
Niagara
#9
Not actual size, but to scale.

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10. ### fireshot91 macrumors 601

Joined:
Jul 31, 2008
Location:
Northern VA
#10
Wouldn't it be trig?

Like the angle levels, and since you have the Hypotenuse?

Tangent of (45)?

11. ### lewis82 macrumors 68000

Joined:
Aug 26, 2009
Location:
Totalitarian Republic of Northlandia
#11
You could, but it requires a scientific calculator, unlike the first method. It's quicker, though.

12. ### LPZ macrumors 65816

Joined:
Jul 11, 2006
#12
Well, I don't need a calculator to do sin(45) = 1/sqrt(2). So the desired length is 1.54"/sqrt(2), or about 1.54"/1.41 = (1.41 + 0.13)/1.41 = 1 + 0.13/1.41, a bit less than 1.10"