Math Question Regarding Aspect Ratio

[Krelmaneck]

It makes sense to me that if you want to get a aspect ratio decimal point, just divide heighth by width. Ok. So as DJ rumpy states 640x480=1.33. Cool. I understand that. That makes sense. But what I dont understand is how in the world does 1.33=4:3?

Because if I try to convert the 1.33 to an aspect ratio format, I get something like 133:100 since

1.33= 1.33/1 x 100/100 = 133/100. Well, that's what I thought at least.

Or did someone just state that the decimal point 1.33 arbitraly=4:3?

Can someone show me the math how 1.33=4:3?

Thanks.

[edDV]

4/3 = 1.33333...

0r 3 x 1.33333 = 4

[Krelmaneck]

4/3 = 1.33333...

0r 3 x 1.33333 = 4

Yes, that's very true that if you multiply every side by 3 because it's a porportion, you would get 4:3 but lets say you did NOT KNOW the original fraction, How would you get from 1.333...to 4/3 if you did not automatically know that the corect fraction to use. I mean a lot of fractions could equal 1.333.


For example, In fact, if I were to start with x=1.3333, if I did not know that x=4/3, how would I get there? That's the real question.

[TJohns]

...I mean a lot of fractions could equal 1.333

True, 640:480 is also 1.33 as you said, it's just that 4:3 uses the smallest integer values. In a similar manner, 1.78 is normal widescreen (16:9) ratio, which I often use to create 512:288 pixel AVI files.

Trev

[turk690]

"A lot of fractions equals 1.333." That's true: 1.333:1, 4:3, 1600:1200, 800:600 are all 1.333, but the smallest integer ratio IS 4:3. "How do I get there?" You just multiply both sides with a common factor that will show the lowest possible integer ratio. That's why, similarly, a lot of fractions equals 1.777. But its lowest integer ratio is 16:9.

[Krelmaneck]

lets take a different route here.... lets say you take the sample matrix of 720x480 which is 1.5, what would be the aspect ratio? Explain why.

[edDV]

720x480 is a storage raster, not a display raster. It is valid for 4:3 or 16:9 factored by display aspect ratio.

For 4:3 multiply 480 x 1.33333 = 640.
So H scaling would be 640/720 = 0.8889

For 16:9 calculate (480/9)x16 = 853.333 ~854 for even numbers
So H scaling would be 854/720 = 1.1861

These numbers are approximate for DVD but not for digital broadcasting which uses a 704x480 transmission raster.

[jagabo]

1.33 AR means 1.33:1

1.33:1 * 2 = 2.66:2
1.33:1 * 3 = 3.99:3 ~= 4:3

You would guess at this point that 1.33 was really 1.333333...

Similarly 1.78 AR means 1.78:1

1.78:1 * 2 = 3.56:2
1.78:1 * 3 = 5.24:3
1.78:1 * 4 = 7.12:4
...
1.78:1 * 9 = 16.02:9

You would guess at this point that the real AR was 16:9.

[dphirschler]

4/3 = 1.33333...

0r 3 x 1.33333 = 4

Yes, that's very true that if you multiply every side by 3 because it's a porportion, you would get 4:3 but lets say you did NOT KNOW the original fraction, How would you get from 1.333...to 4/3 if you did not automatically know that the corect fraction to use. I mean a lot of fractions could equal 1.333.


For example, In fact, if I were to start with x=1.3333, if I did not know that x=4/3, how would I get there? That's the real question.

just reduce the fraction:

640x480 = 64x48 = 8x6 = 4x3

You can use algebra to get everything else:

640/480=1.33...
4/3=1.33...

w/h=a
h*a=w
w/a=h


Darryl

[dphirschler]

Here is a spreadsheet I use with regards to aspect ratio.


Darryl

display%20aspect%20ratio%20calc_v1.1.xls

[Krelmaneck]

1.33 AR means 1.33:1

1.33:1 * 2 = 2.66:2
1.33:1 * 3 = 3.99:3 ~= 4:3

You would guess at this point that 1.33 was really 1.333333...

Similarly 1.78 AR means 1.78:1

1.78:1 * 2 = 3.56:2
1.78:1 * 3 = 5.24:3
1.78:1 * 4 = 7.12:4
...
1.78:1 * 9 = 16.02:9

You would guess at this point that the real AR was 16:9.

Beautifully explained! This is what I was looking for! Now, I can understand that these numbers are not random numbers chosen for aspect ratio. And to proove I understand this I will explain how 2.20=11:5


2.20 can also be written as 2.20:1

And if factors are:

2.20:1 x 2 = 4.4:2 = 2
2.20:1 x 3 = 6.6:3 = 2.3
2.20:1 x 4 = 8.8/4 = 2.25
2.20:1 x 5 = 11:5 = 2.20


the lowest combination that is equal to that of 2.20 with the lowest factor is 5 (ie 2.20:1 x 5 = 11:5 = 2.20)


therefore 2.20:1=11:5


Thank you very much for your help people. This discussion is closed. I will have more topics regarding aspect ratio but jagabo has given me the answer so that I can understand it. Also thanks to dphirschler who gave me the link to the spreadsheet and to eveyone who participated in this topic.

--Derek