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Diagonal of Golden Rectangle given perimeter Solution

STEP 0: Pre-Calculation Summary
Formula Used
diagonal = sqrt(((Perimeter/(2*(1+(1/[phi]))))^2)*(1+(1/[phi]^2)))
d = sqrt(((P/(2*(1+(1/[phi]))))^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
Perimeter - The perimeter of a figure is the total distance around the edge of the figure. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Perimeter: 20 Meter --> 20 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d = sqrt(((P/(2*(1+(1/[phi]))))^2)*(1+(1/[phi]^2))) --> sqrt(((20/(2*(1+(1/[phi]))))^2)*(1+(1/[phi]^2)))
Evaluating ... ...
d = 7.26542528005361
STEP 3: Convert Result to Output's Unit
7.26542528005361 Meter --> No Conversion Required
FINAL ANSWER
7.26542528005361 Meter <-- Diagonal
(Calculation completed in 00.000 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 given perimeter Formula

diagonal = sqrt(((Perimeter/(2*(1+(1/[phi]))))^2)*(1+(1/[phi]^2)))
d = sqrt(((P/(2*(1+(1/[phi]))))^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 given perimeter?

Diagonal of Golden Rectangle given perimeter calculator uses diagonal = sqrt(((Perimeter/(2*(1+(1/[phi]))))^2)*(1+(1/[phi]^2))) to calculate the Diagonal, The Diagonal of golden rectangle given perimeter 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 given perimeter using this online calculator? To use this online calculator for Diagonal of Golden Rectangle given perimeter, enter Perimeter (P) and hit the calculate button. Here is how the Diagonal of Golden Rectangle given perimeter calculation can be explained with given input values -> 7.265425 = sqrt(((20/(2*(1+(1/[phi]))))^2)*(1+(1/[phi]^2))).

FAQ

What is Diagonal of Golden Rectangle given perimeter?
The Diagonal of golden rectangle given perimeter 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(((P/(2*(1+(1/[phi]))))^2)*(1+(1/[phi]^2))) or diagonal = sqrt(((Perimeter/(2*(1+(1/[phi]))))^2)*(1+(1/[phi]^2))). The perimeter of a figure is the total distance around the edge of the figure.
How to calculate Diagonal of Golden Rectangle given perimeter?
The Diagonal of golden rectangle given perimeter 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(((Perimeter/(2*(1+(1/[phi]))))^2)*(1+(1/[phi]^2))). To calculate Diagonal of Golden Rectangle given perimeter, you need Perimeter (P). With our tool, you need to enter the respective value for Perimeter 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 Perimeter. 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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