# THE SILVER RATIO: WHY JAPANESE ARCHITECTURE IS SO BEAUTIFUL

By Ethan Cheng

The Golden Ratio is widely known as the divine proportion that was applied to some of the most widely known architectures known today, such as the Pyramids of Giza and the Pantheon. However, Asian architecture makes use of another ‘divine proportion’, namely the Silver Ratio. While the Golden Ratio (1.618034) is symbolized by the Greek letter φ, the Silver Ratio is denoted by δS . Two quantities are in Silver Ratio if the ratio of the sum of the lesser and twice of the greater, to the greater quantity, is the same as the ratio of the greater to the lesser, in algebraic terms, (2a+b)/a = a/b ≡ δS . When one puts this into a ratio, the proportion is 1:√2, which is approximately 1:1.414. In Japan, the silver ratio has been considered to be the most beautiful proportion and is called 大和比 (yamato-hi, meaning ‘Japanese Proportion’). It has been used in structures from various periods, and it has also been used on the faces of Buddha statues. One recognizable application of the Silver Ratio is on pagodas and temples, such as the Horyu-ji (法隆寺 ) Temple, where the width of the larger roof is in Silver Ratio with the subsequently smaller roof above. A modern example of the Silver Ratio in Japanese Architecture is the Tokyo Skytree, where the distance between the ground and the second observatory is in Silver Ratio to the distance between the ground and the top of the tower. Of course, this may be a coincidence as modern architecture is less concerned on divine proportion, but the fact that the Silver Ratio is present makes the building look naturally balanced and aesthetically pleasing.