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  1. A family $X \to S$ is just a flat morphism of varieties. The "members" of the family are the fibers $X_s$ above the points $s \in S$. Intuitively, the flatness of the morphism says that the members of the family look alike.

  2. Jan 14, 2024 · The term ‘origin’ comes from the Latin word ‘originem’, implying ‘the beginning’, ‘source’, or ‘birth’. From a universal viewpoint, the origin is characterized as the point where all coordinates are zero. In a broader perspective, the origin acts as a reference point – a place from where measurements begin or are considered to start.

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  4. Geometry was started in ancient Greece by Euclid, who wrote the Elements around 300 BC. Other Greek mathematicians such as Archimedes and Pythagoras also made important contributions to the subject. Geometry was later developed by Arab mathematicians in the Middle Ages and by European mathematicians in the Renaissance.

  5. Family of origin meaning refers to the concept that our family of origin, or the family we were born into, plays a significant role in shaping who we are as individuals. It encompasses the beliefs, values, traditions, and dynamics that are passed down from generation to generation within a family unit.

  6. A family of curves is a set of curves, each of which is given by a function or parametrization in which one or more of the parameters is variable. In general, the parameter (s) influence the shape of the curve in a way that is more complicated than a simple linear transformation.

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