Geometry does not expose the physical world, but it does tell us something about how the physical world works. Geometry is relevant to the physical world.
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Each cut exposes new surface (that was previously in the interior of the cube) without changing the total volume, so yes. If you have two numbers, and one of them changes when the other doesn't, the ratio between the two numbers will change.
It segments the market by measurable characteristics such as gender and age. The demographic dimensions normally used by marketers are usually, age, gender, family structure, income, life-cycle stage, race and religion. It works on the premise that customer wants are closely linked to variables such as age and income. Psychographic segmentation is a method of dividing markets on the bases of the psychology and lifestyle habits of customers. It segments customers in terms of shared activities, lifestyle choices, interests and opinions. Psychographic segments usually include demographic information such as age or gender, but the richer descriptions emerge so well beyond these characteristics. Attitude to risk, socio-economic groups an lifestyle are the most commonly used methods of psychographic segmentation. In other words demographics has more to do with who people are, pyschographics has more to do with people's lifestyle choices and opinions