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The Golden Ratio is an irrational number which is around about 1.61803398875
The Golden Ratio is an irrational number which is around about 1.61803398875
Like pi the digits go on forever
Like pi the digits go on forever
Often phi (φ) is approximated as 1.62
Often phi (φ) is approximated as 1.62
φ is famous in Nature, Art and Design
φ is famous in Nature, Art and Design
Using Inkscape to explore the Fibonacci Series and discover φ
Using Inkscape to explore the Fibonacci Series and discover φ
Turn on the grid view>page grid
Hold control whilst you use the rectangle tool to draw a small square in the middle of the page (the red 1 in the centre), aligned with the grid.
Select the small red square and duplicate it with control-D
Drag the duplicate square under the first red square and colour it yellow (the yellow 1 exactly under the red one)
Hold control whilst you use the rectangle tool again to draw another square starting from the top right vertex of the red 1, and finishing when it matches the edge length of 1red + 1yellow. Colour it green.
Carry on to add the blue 3, the purple 5, the red 8, the yellow . . . . . . .
The Maths
The Maths
The edge length of each of the first two squares is one unit, the edge of the third square is the first two added together so has width of 2 units
The forth square has an edge length of square 2 plus the first 1 , so has an edge length of 3
the next edges are 5 and then then 8, then 13, then 21, then 34 . . . .
This series of numbers 0,1,1,2,3,5,8,13,21,34 . . . . is called the Fibonacci Series
This series of numbers 0,1,1,2,3,5,8,13,21,34 . . . . is called the Fibonacci Series
Starting with 0 and 1, each new number in the sequence is simply the sum of the two before it.
Using Excel
Using Excel
Using Excel we can show shows how the ratios of the successive numbers in the Fibonacci sequence quickly converge on Phi. After the 40th number in the sequence, the ratio is accurate to 15 decimal places.
In Inkscape draw quarter circles over each square of the Fibonacci sequence. Now you have the famous Golden spiral.
In Inkscape draw quarter circles over each square of the Fibonacci sequence. Now you have the famous Golden spiral.
Alternative drawing method: Lets use phi in design with Inkscape: http://goinkscape.com/the-golden-ratio-in-inkscape-design/
Alternative drawing method: Lets use phi in design with Inkscape: http://goinkscape.com/the-golden-ratio-in-inkscape-design/
The Fibonacci Sequence and Golden Ratio in Scratch
The Fibonacci Sequence and Golden Ratio in Scratch
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