What part of the Constitution mandated the census?

Article one, section 2 clause 3 is what you are looking for. This section of the constitution outlines the way in which members of the house of representatives shall be apportioned. The constitution mandates that every 10 years every citizen be counted. This is were the census comes in. The census determines the population of the states and thereby the number of representatives that state receives in the house. The constitution does not specifically identify how many citizens count as one seat in the house but rather lays out the restriction that no state shall have more than one member for every 30,000 citizens. Currently the ration is approximately 1 representative for every 700,000 citizens. Also, every state shall have at least one seat in the house, regardless of that states population.

Each state then takes the census figures and determines how the state will be divided to denote each house seats area of representation. This is different from state to state but most leave it up to the states legislature to determine how the districts shall be divided. This at times can lead to politically charged situations in which one party will try to extend the borders of a favorable district into one that is controlled by the opposing party in order to make it difficult for their opponents to get reelected. This is known as gerrymandering.