## History and applications

### An application to film and video

In modern film and video, one has the power to vary the width and height of the images being filmed and replayed. The ratio between the width and height of an image is called its aspect ratio. This ratio is commonly expressed in the form $$x:y$$.

The most common aspect ratio used in movie theatres is $$2.35:1$$, while the aspect ratio traditionally used for television and video is $$4:3 \approx 1.33:1$$. It was found that the geometric mean of the numbers 2.35 and 1.33 provides a good compromise between the two different aspect ratios, distorting or cropping both in some sense equally. The geometric mean of 2.35 and 1.33 is approximately 1.77, and the ratio $$1.77:1$$ corresponds approximately to $$16:9$$. This is the aspect ratio adopted by the Society of Motion Picture and Television Engineers, and used for high-definition digital television.

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