Pythagorean Potato Hoe

The Pythagorean Potato Hoe is a Hoe. It can be crafted from the Mathematical Hoe Blueprint. This hoe can be upgraded with Jacob's Tickets, Potatoes, Enchanted Potatoes, & Enchanted Baked Potatoes, and can get higher tiers by harvesting crops. With use of a Recombobulator 3000, this hoe can reach a maximum Rarity of.

Upgradeable
Harvest +10% Potato Gain +1% Farming Exp
 * -|Common Stats=

Harvest +25% Potato Gain +2% Farming Exp Logarithmic Counter = Harvest +16% Potato per digits on the Counter, minus 4! Bonus Potato percent increases your Farmhand perk's chances
 * -|Uncommon Stats=

Harvest +50% Potato Gain +3% Farming Exp Logarithmic Counter = Harvest +16% Potato per digits on the Counter, minus 4! Collection Analysis = Harvest +8% Potato per digits of your collection, minus 4! Bonus Potato percent increases your Farmhand perk's chances
 * -|Rare Stats=

Tiers
Harvest +10% Potato Gain +1% Farming Exp
 * -|Common Stats=

Harvest +25% Potato Gain +2% Farming Exp
 * -|Uncommon Stats=

Harvest +50% Potato Gain +3% Farming Exp Reach 1M Counter for +1 Rarity!
 * -|Rare Stats=

Harvest +50% Potato Gain +5% Farming Exp Reach 10M Counter for +1 Rarity!
 * -|Epic Stats=

Harvest +50% Potato Gain +8% Farming Exp
 * -|Legendary Stats=

Harvest +50% Potato Gain +12% Farming Exp
 * -|Mythic Stats=

Formulas
The number of digits on the counter may be calculated using:
 * $$n = \left\lfloor\log_{10} counter\right\rfloor + 1$$

In order to mathematically represent the and  ability scaling, the following formula has to be used:
 * $$\text{Logarithmic Counter Bonus} =

\begin{cases} 0 & n \leq 4 \\ (n - 4) \times 16% & otherwise \end{cases}$$
 * $$\text{Collection Analysis Bonus} =

\begin{cases} 0 & n \leq 4 \\ (n - 4) \times 8% & otherwise \end{cases}$$

Trivia

 * Since the introduction of Farming Fortune, all bonuses are applied as Farming Fortune as well, converting its previously multiplicative bonuses into additive bonuses.
 * The Rarity will increase by 1, whether you are upgrading it through crafting, or by counter(collecting potatoes). All 3 upgrades, and all 3 counter tiers are obtainable for the hoe, no matter the order you do them in. For example, if you have a Pythagorean Potato Hoe with 100k counter, it will increase to, and then you can increase it to by using the crafting recipe for , listed above, under "Upgradeable." The order you do them in does not matter, the Rarity will always increase by 1.