If you read this page to its conclusion the terms Golden Mean and Fibonacci number will be defined.
To use this page, add an integer to the form and click on the Submit Query button. The Fibonacci sequence of the number you enter and of that number plus 1 will be calculated and displayed. Then the ratio of the two Fibonacci numbers will be calculated and a rectangle with this aspect ratio will be drawn on the page. An ellipse is displayed at the center of the rectangle. This ellipse will be a perfect circle if the rectangle matches the Golden Mean.
- The Romans were big believers in standardized ideals of beauty. They had a concept of a perfect rectangle, which had an aspect ratio of 1: 1.6180. They called this ratio the Golden Mean. The Golden Mean is a pattern that frequently occurs in nature.
- The Fibonacci number series progresses thusly: 0, 1, 1, 2, 3, 5, 8, 13, 21,… and so forth. Each successive number in the series is the sum of the preceding two numbers in the series. The ratio of the 13th number in the series (Counting from Fibonacci 1, not Fibonacci 0.) to the 14th number in the series is equivalent to the Golden Mean. This relationship also holds true for higher numbers in the series, but not for lower numbers in the series. The Fibonacci series can be described as a spiral pattern.
- Please note that while the Golden Mean is calculated to a precision of 0.0001, the rectangle graphic only resolves to a precision of 0.0044.