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2. Pyramid (geometry) - Wikipedia

   en.wikipedia.org/wiki/Pyramid_(geometry)

   The volume of a pyramid was recorded back in ancient Egypt, where they calculated the volume of a square frustum, suggesting they acquainted the volume of a square pyramid. [30] The formula of volume for a general pyramid was discovered by Indian mathematician Aryabhata, where he quoted in his Aryabhatiya that the volume of a pyramid is ...

3. Tetrahedron - Wikipedia

   en.wikipedia.org/wiki/Tetrahedron

   The volume of a tetrahedron can be obtained in many ways. It can be given by using the formula of the pyramid's volume: =. where is the base' area and is the height from the base to the apex. This applies for each of the four choices of the base, so the distances from the apices to the opposite faces are inversely proportional to the areas of ...

4. List of formulas in elementary geometry - Wikipedia

   en.wikipedia.org/wiki/List_of_formulas_in...

   Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities; List of volume formulas – Quantity of three-dimensional space

5. Frustum - Wikipedia

   en.wikipedia.org/wiki/Frustum

   The Egyptians knew the correct formula for the volume of such a truncated square pyramid, but no proof of this equation is given in the Moscow papyrus. The volume of a conical or pyramidal frustum is the volume of the solid before slicing its "apex" off, minus the volume of this "apex":

6. Solid angle - Wikipedia

   en.wikipedia.org/wiki/Solid_angle

   The solid angle of a four-sided right rectangular pyramid with apex angles a and b (dihedral angles measured to the opposite side faces of the pyramid) is = ⁡ (⁡ ⁡ ()). If both the side lengths ( α and β ) of the base of the pyramid and the distance ( d ) from the center of the base rectangle to the apex of the pyramid (the center of ...

7. Square pyramid - Wikipedia

   en.wikipedia.org/wiki/Square_pyramid

   In general, the volume of a pyramid is equal to one-third of the area of its base multiplied by its height. [8] Expressed in a formula for a square pyramid, this is: [9] =. Many mathematicians have discovered the formula for calculating the volume of a square pyramid in ancient times.

8. Pyramidal number - Wikipedia

   en.wikipedia.org/wiki/Pyramidal_number

   The term often refers to square pyramidal numbers, which have a square base with four sides, but it can also refer to a pyramid with any number of sides. [2] The numbers of points in the base and in layers parallel to the base are given by polygonal numbers of the given number of sides, while the numbers of points in each triangular side is ...

9. Regular polyhedron - Wikipedia

   en.wikipedia.org/wiki/Regular_polyhedron

   This definition rules out, for example, the square pyramid (since although all the faces are regular, the square base is not congruent to the triangular sides), or the shape formed by joining two tetrahedra together (since although all faces of that triangular bipyramid would be equilateral triangles, that is, congruent and regular, some ...