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Diagonal of Golden Rectangle Solution

STEP 0: Pre-Calculation Summary
Formula Used
diagonal = sqrt((Long edge^2)*(1+(1/[phi]^2)))
d = sqrt((a^2)*(1+(1/[phi]^2)))
This formula uses 1 Constants, 1 Functions, 1 Variables
Constants Used
[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Long edge - Long edge is the longest boundary line of a surface or plane. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Long edge: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d = sqrt((a^2)*(1+(1/[phi]^2))) --> sqrt((10^2)*(1+(1/[phi]^2)))
Evaluating ... ...
d = 11.7557050458495
STEP 3: Convert Result to Output's Unit
11.7557050458495 Meter --> No Conversion Required
FINAL ANSWER
11.7557050458495 Meter <-- Diagonal
(Calculation completed in 00.016 seconds)

4 Diagonal of Golden Rectangle Calculators

Diagonal of Golden Rectangle given area
diagonal = sqrt(((sqrt(Area*[phi]))^2)*(1+(1/[phi]^2))) Go
Diagonal of Golden Rectangle given perimeter
diagonal = sqrt(((Perimeter/(2*(1+(1/[phi]))))^2)*(1+(1/[phi]^2))) Go
Diagonal of Golden Rectangle given short side
diagonal = sqrt(((Short edge*[phi])^2)*(1+(1/[phi]^2))) Go
Diagonal of Golden Rectangle
diagonal = sqrt((Long edge^2)*(1+(1/[phi]^2))) Go

Diagonal of Golden Rectangle Formula

diagonal = sqrt((Long edge^2)*(1+(1/[phi]^2)))
d = sqrt((a^2)*(1+(1/[phi]^2)))

What is a golden rectangle?

In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, 1:1+sqrt(5)/2 which is 1:phi is approximately 1.618. Golden rectangles exhibit a special form of self-similarity: All rectangles created by adding or removing a square are Golden rectangles as well. A distinctive feature of this shape is that when a square section is added—or removed—the product is another golden rectangle, having the same aspect ratio as the first. Square addition or removal can be repeated infinitely, in which case corresponding corners of the squares form an infinite sequence of points on the golden spiral, the unique logarithmic spiral with this property. Diagonal lines drawn between the first two orders of embedded golden rectangles will define the intersection point of the diagonals of all the embedded golden rectangles; Clifford A. Pickover referred to this point as "the Eye of God"

How to Calculate Diagonal of Golden Rectangle?

Diagonal of Golden Rectangle calculator uses diagonal = sqrt((Long edge^2)*(1+(1/[phi]^2))) to calculate the Diagonal, The Diagonal of golden rectangle formula is defined as a straight line joining two opposite corners of the golden rectangle , where diagonal = diagonal of golden rectangle , side_a =long side of golden rectangle. Diagonal and is denoted by d symbol.

How to calculate Diagonal of Golden Rectangle using this online calculator? To use this online calculator for Diagonal of Golden Rectangle, enter Long edge (a) and hit the calculate button. Here is how the Diagonal of Golden Rectangle calculation can be explained with given input values -> 11.75571 = sqrt((10^2)*(1+(1/[phi]^2))).

FAQ

What is Diagonal of Golden Rectangle?
The Diagonal of golden rectangle formula is defined as a straight line joining two opposite corners of the golden rectangle , where diagonal = diagonal of golden rectangle , side_a =long side of golden rectangle and is represented as d = sqrt((a^2)*(1+(1/[phi]^2))) or diagonal = sqrt((Long edge^2)*(1+(1/[phi]^2))). Long edge is the longest boundary line of a surface or plane.
How to calculate Diagonal of Golden Rectangle?
The Diagonal of golden rectangle formula is defined as a straight line joining two opposite corners of the golden rectangle , where diagonal = diagonal of golden rectangle , side_a =long side of golden rectangle is calculated using diagonal = sqrt((Long edge^2)*(1+(1/[phi]^2))). To calculate Diagonal of Golden Rectangle, you need Long edge (a). With our tool, you need to enter the respective value for Long edge and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Diagonal?
In this formula, Diagonal uses Long edge. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • diagonal = sqrt((Long edge^2)*(1+(1/[phi]^2)))
  • diagonal = sqrt(((Short edge*[phi])^2)*(1+(1/[phi]^2)))
  • diagonal = sqrt(((Perimeter/(2*(1+(1/[phi]))))^2)*(1+(1/[phi]^2)))
  • diagonal = sqrt(((sqrt(Area*[phi]))^2)*(1+(1/[phi]^2)))
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