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.
In Walter's Lab Notes, Walter refers to the shape of the room containing the laboratory without specifying what the shape is.
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.
Walter uses this math again to determine the origin phenomenon of the expanding time bubbles and colliding timelines.
Phi appears on the Frog Glyph. Fibonacci Spirals and the number 1.6180339887... also appear alongside other glyphs.