Phi

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Phi (Φ and φ, pronounced [fī]) is a Greek letter. In mathematics it is used to represent the number 1.6180339887..., the key number in the Golden Ratio. Many living organisms grow according to the golden ratio; the bones in a human finger are proportioned in a ratio of approximately 1:1.6; the branching of veins and nerves in animals and humans follow similar proportions. Phi is an essential number when calculating the dimensions of a Fibonacci Spiral.

Pilot

  The number 1.61803 appears on the side of the kayak Olivia Dunham sees in her dream during the Synaptic Transfer with John Scott.

The Same Old Story

  In Walter's Lab Notes, the image includes a grilled cheese sandwhich that has been nibbled into a shape approximating golden rectangle dimensions.

The Ghost Network

  In Walter's Lab Notes, Walter refers to the shape of the room containing the laboratory without specifying what the shape is.

Safe

  In the hotel where they are staying, Peter asks Walter about the numbers he recites as he is falling asleep. Walter explains that it is Fibonacci. Soon after, they realize that the numbers relate to the safety deposit boxes that are being robbed in their current investigation. Knowledge of the sequence allows them to set a trap at the next logical location in the pattern.

And Those We've Left Behind

  Walter uses this math again to determine the origin phenomenon of the expanding time bubbles and colliding timelines.

Trivia

  Phi appears on the Frog Glyph. Fibonacci Spirals and the number 1.6180339887... also appear alongside other glyphs.