In what ways does the united states constitution manifest the principles of both republican and democratic forms of government? in what ways does it deviate from those principles?

The United Constitution manifest principles of democracy through citizens voting for their representatives.  It represents republicanism through shared power between the federal and state power. A powerful central government is a departure from republicanism. The electoral college is a departure from democracy through majority rule

theodore roosevelt challenged william to a duel, whoever won, got their policy sent to congress. it ended up in a stalemate, and both men were injured and sent to the hospital.

consider an orange peel: if you want to try and lay it flat, you have to stretch it, we know exactly how things are being stretched or squashed at any given point. we have many different map projections because each has different patterns of some projections can even preserve certain features of the earth without