Mathematician gains more gold based on how many times he has gained gold since he last died.
Golden Ratio is an ability.
Gold gain equation: (φ^n - (1 - φ)^n)/√5, where n = times gold has been gained since death and φ is the golden ratio.
This yields the nth Fibonacci number.
COST: 40 / 50 / 60 / 70 / 80 mana
Active: After a short cast time, Mathematician launches 10 bolts that oscillate between spreading out evenly to 750 units across and converging every 314 units, starting together. Each bolt passes through minions and small monsters, but stops at terrain, champions, and large and epic monsters, dealing magic damage when they initially make contact with enemies. Additionally, they are 300 units long, dealing magic damage to enemies inside them every 0.25 seconds. Each bolt deals its own damage.
Active: Mathematician creates a 1200-length line perpendicular to the direction he cast this ability for 5 seconds, which is attached to himself, but always stays the same orientation. All projectiles passing through this line push the section of line they pass through a distance, based on their speed, in the direction they were headed. This persists at his death location if he dies before the ability ends.
When there is only one second left, one side of the line is designated as damaging and the other as healing, based on how many enemies are inside the areas between the initial line and the current line, and it detaches from Mathematician. More enemies means that side becomes damaging. At the end of the 5 seconds, units in the area between the initial line and the current line either take damage or are healed, based on what side they are on.
Active: Mathematician places down a 600-length line for 2.5 seconds that makes any enemy damaging projectiles heal for the amount they would have damaged for and makes any healing projectiles deal true damage equal to the amount they would have healed for. Additionally, any healing or damaging done by projectiles passing through the line is amplified and projectiles hit the team they would have hit before being inverted.
Active: Mathematician calculates the average of the maximum healths of all targets in an area and sets the health of all targets hit to an amount relative to the average based on their distance from the center of the area after a 1.5 second warning. This will grant a permanent shield if the amount it is getting set to is larger than the target's maximum health.