We present and apply to data for insects, chickens and rats a conceptual and experimental framework for studying nutrition as a multi-dimensional phenomenon. The framework enables the unification within a single geometrical model of several nutritionally relevant measures, including: the optimal balance and amounts of nutrients required by an animal in a given time (the intake target), the animal's current state in relation to these requirements, available foods, the amounts of ingested nutrients which are retained and eliminated, and animal performance. Animals given a nutritionally balanced food, or two or more imbalanced but complementary foods, can satisfy their nutrient requirements, and hence optimize performance. However, animals eating noncomplementary imbalanced foods must decide on a suitable compromise between overingesting some nutrients and underingesting others. The geometrical models provide a means of measuring nutritional targets and rules of compromise, and comparing these among different animals and within similar animals at different developmental stages or in different environments. They also provide a framework for designing and interpreting experiments on the regulatory and metabolic mechanisms underlying nutritional homeostasis.