Credit cards are in the shape of a Golden Rectangle. If you ever need an easily accessible example of a golden rectangle illustrating the proportions of the golden section, all you need do is to pull out a credit card or drivers license.

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Standard sized credit cards are 54mm by 86mm, creating a ratio of 0.628, less than a millimeter off from a perfect golden ratio or golden section of 0.618, the reciprocal of 1.618.

Sandeep says

I was looking for the standard size of Credit card. Are you sure the size you have mentioned is correct!!

Gary B Meisner says

Yes. See https://en.wikipedia.org/wiki/ISO/IEC_7810. The official US size is 53.98 x 85.60 mm, so the 54×86 stated is correct to within fractions of a millimeter. It’s not exactly a golden ratio, but close enough for making quick very close approximations.

The Golden Mean or Ratio appears in mathematics and in nature. https://en.wikipedia.org/wiki/Golden_ratio

See also our articles on mathematics, life and beauty.

The above-stated credit-card dimensions differ from the golden ratio by about 2%..

If the golden ratio were intended, then there wouldn’t be that 2% departure from the golden ratio.

But the close similarity suggests that maybe that shape is perceived as neither too long nor too short

Michael Ossipoff

As an update, after this article was first written, ISO standards were released in 2003 that state the dimensions of a credit card to be 85.60 mm x 53.98 mm. These numbers were apparently converted from the English sizes 3 3/8″ x 2 1/8″. The golden ratio of 85.60 is 52.90. So while that is a 2% difference, it’s only a difference of only 1 mm. This is not visibly perceptible, so the credit card still serves as a nice, handy reference for evaluating golden ratio measurements.

It’s a near perfect Golden Rectangle

86mm : 53,75mm

I don not think Phi determines the ratio of a true golden rectangle, that’s reverse thinking.

21/13, for instance, is a perfect golden rectangle; not 21,034/13, which is closer to Phi. (1,618)

You appear to be confusing a Fibonacci spiral with a Golden Spiral. The Fibonacci spiral has rectangles and rectangles based on Fibonacci numbers, such as 21 and 13. This only approximates a Golden Spiral, which is comprised of true Golden Rectangles. A Golden Rectangle has sides in the ratio of Phi (1.618…) to 1.

According to the definition of a Golden Rectangle you are right. (A Golden Rectangle is a rectangle whose width is to its length as the length is to the sum of the width and length).

Unfortunately such a rectangle is just an ideal; it is completely irrational. 😉

Being irrational really has no impact on our ability to apply the concept. A 1″ square is “just an ideal” too, because in practice it will never be EXACTLY 1.000…” with an infinite number of zeros.

That’s just the nature of the physical world in which we live, and there’s nothing unfortunate about it. We can apply mathematical concepts with as much accuracy as needed, and that’s rarely beyond about 5 decimal places.

I assume we agree, that the credit card can be considered golden even thought it does not exactly match the (in)definite golden standard: 1,618..x 2,618.

I tend towards a more discrete definition of the golden rectangle as rabbits do not produce fractions.

We have to be careful to not call anything that comes close to 1.618 to be an application of the golden ratio. Conversely we shouldn’t say that an informed intentional application of the golden ratio, executed with reasonable accuracy, is not a golden ratio because it wasn’t done with infinite precision.

The problem with the “discrete” application based on integers and rabbits is that it is highly inaccurate early in the series. The ratios of the first successive Fibonacci number pairs are 1, 2, 1.5, 1.6 and 1.625. It’s not until you get to Fibonacci numbers of 21 and higher that you get ratios that I would consider close enough to be considered “golden.” The first Fibonacci sequence pair to produce 1.618… is 233/144. That’s a LOT of rabbits!!!

I just don’t think that I am the one who is ‘confusing’ the Golden Rectangle with a Fibonacci one. Seems to me they are one and the same. I understand that the ratio is primarely quite ‘far’ of from being golden, but are it not the Fibonacci numbers themselves that have the unique interwoven property that generates the golden ratio.. Even if you take 2 Lucas numbers for instance; they still grow in the same ratio:

3+4

3+4+4

3+3+4+4+4

Or any number

Anyway, thank you for your brilliant site.

A Fibonacci spiral and Golden spiral are similar, but uniquely different, as shown here: https://www.goldennumber.net/spirals/

The Golden rectangle of the Golden spiral is always the same in its proportions. There is but one!

The Fibonacci rectangles of the Fibonacci spiral though change in proportion with every new set of Fibonacci numbers, and there are an infinite number of them. So if we refer to a “Fibonacci rectangle” which one do we mean? The Fibonacci rectangles get closer and closer to the Golden rectangle as the series progresses, but it’s never the same as the Golden rectangle.

I’ve not heard though of an

It is rather doubtfull to state the ratio changes while the the initial difference of 1 is ‘nihilated’. The definition of the ratio’s becomming one is not an exclusive one as this also acoounts for all 1/x + n recursions.

ps. no more dan 13 rabbits are needed to come closer to phi than with a creditcard.

5/8 – 0,618033 = 0,006967

53,98/85,60 – 0,618033 = 0,012574

The comment-box is 5,60 x 2,85 on my device; that’s too far off 😉

A bonus feature is that 5+3 and 8+5 are sums of Fibonacci-numbers.. Using inches (3 3⁄8 × 2 1⁄8), the ratio is 34/54. Only one count off