The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire word signifies a great woman. What is the word?

Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?

A saga of thought, a guess in disguise, where science dances on the edge of surprise, dreams of possibilities in her elegant robe, before truth's needle threads her globe.

A rich man needs it, a poor man has it, if we eat it, we die, and when we die, we bring it with us.

I sound like a dessert or bodily waste depending on how you pronounce me. I am important in geometry. I have a day named in my honor. I have a very famous specific set of numbers.