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Update about.html
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about.html

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},
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"dateCreated": "2024-08-31",
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"datePublished": "2024-08-31",
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"dateModified": "2025-11-11",
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"dateModified": "2025-11-14",
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"description": "About the context of the Core Geometric System ™, the best-established and most accurate framework to calculate area and volume.",
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"disambiguatingDescription": "Exact, empirically grounded and rigorously proven formulas over the conventional approximations.",
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"headline": "Introducing the Core Geometric System ™",
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<p style="margin:12px;">The commonly used base × height / 3 approximation for the volume of a pyramid was likely estimated based on two observations.
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One is that the area of the mid-height cross section of a regular pyramid - of which's apex can be connected to the midpoint of the base with a perpendicular line - is exactly a quarter of a circumscribed solid's with the same base and height.
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One is that the area of the mid-height cross section of a regular pyramid of which's apex can be connected to the midpoint of the base with a perpendicular line is exactly a quarter of a circumscribed solid's with the same base and height.
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That makes the ratio between the mid-height cross-sectional area of the pyramid, and the difference between the mid-height cross-sectional areas of the circumscribed solid and the pyramid 1 : 3 .
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The same is true for a cone.
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Can this ratio can be generalized for the overall volume of any cone and pyramid?
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Can this ratio be generalized for the overall volume of any cone and pyramid?
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No. Because it's not true in case of most other shapes.
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- height is e,
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then the volume of each pyramid has to be larger than 1/3 × base × height, because 3 such pyramids can't form a cube with the same edge length, because their vertices and faces can't occupy the same space simultaneously.
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then the volume of each pyramid has to be larger than 1 / 3 × base × height, because 3 such pyramids can't form a cube with the same edge length, because their vertices and faces can't occupy the same space simultaneously.
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The vertices are the most obvious examples, but the same is true for the edges, the diagonals and the inner faces.

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