- From: Christoph Päper via GitHub <sysbot+gh@w3.org>
- Date: Thu, 30 Jan 2020 07:18:43 +0000
- To: public-css-archive@w3.org
Golden rectangles would probably be a major use case. Since many graphic designers demand pixel-perfect layouts across devices and browsers, Iʼd say a reasonable approximation of φ would yield accurate results for all integer base edges up to, say, `2000px`, because larger values are very rarely useful. This would stay accurate, if one could correct initial errors by always rounding in the same way. Alas, with 8:5, a rectangle 100px wide would be 160px tall instead of 161px and rounding could not help at all. The first approximation of φ by the ratio of two adjacent Fibonacci numbers that is … - … better than 17/12 and 24/17 for √2 or `sqrt(2)` (i.e. 100.17% and 99.83%) is f~8~/f~7~ = 21/13 ≈ 1,615385. - … better than 22/7 for π or `pi` (i.e. 100.04%) is f~10~/f~9~ = 55/34 ≈ 1.617647. - … correct to 3 decimal places (with truncation, no rounding) is f~11~/f~10~ = 89/55 = 1.6(18). - … correct to 4 decimal places is f~13~/f~12~ = 233/144 = 1.6180(5). - … correct to 5 decimal places is f~15~/f~14~ = 610/377 ≈ 1,618037. - … correct to 6 decimal places is f~18~/f~17~ = 2584/1597 ≈ 1,6180338. By the way, a static function to return the *n*-th Fibonacci number _could have been_ a reasonable substitute to `phi` as a constant, e. g.: `fibonacci(3)` = `3`.The actual sequence could also have been up to a parameter, e. g.: `seq(prime, 3)` = `seq(fibonacci, 4)` = `5` with `seq(prime, 0)` = `seq(fibonacci, 0)` = `seq(fibonacci, 1)` = `1`. -- GitHub Notification of comment by Crissov Please view or discuss this issue at https://github.com/w3c/csswg-drafts/issues/4702#issuecomment-580116714 using your GitHub account
Received on Thursday, 30 January 2020 07:18:45 UTC