An aspect ratio defines the ratio of an image's width to its height. An aspect ratio can remain constant even if the actual size of an image changes. The formula for aspect ratio is width divided by height. Most of the images on this site are 1400px wide by 1000px hight. 1400/1000=1.4.... meaning the width of the image is 1.4 times the height.
If I want to use images that are 500px high but keep the same ratio, I would multiply 500px x 1.4 = 700px. Likewise, if I want to use images that are 700 px tall, I would divide it by 1.4 = 500px.
If a rectangle has a ratio of 1.618, it has a golden ratio. The golden ratio can be calculated by hand or by using a golden rectangle calculator. If I use images that are 1000px high, to have a golden ratio I would need a width of 1618.034. Reduced by half, the image would be 500px high by 809px wide (I ignored a tiny 0.017 given with the width).