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  2. Rectangle packing - Wikipedia

    en.wikipedia.org/wiki/Rectangle_packing

    Maximum disjoint set (or Maximum independent set) is a problem in which both the sizes and the locations of the input rectangles are fixed, and the goal is to select a largest sum of non-overlapping rectangles. In contrast, in rectangle packing (as in real-life packing problems) the sizes of the rectangles are given, but their locations are ...

  3. Packing problems - Wikipedia

    en.wikipedia.org/wiki/Packing_problems

    For example, it is possible to pack 147 rectangles of size (137,95) in a rectangle of size (1600,1230). Packing different rectangles in a rectangle : The problem of packing multiple rectangles of varying widths and heights in an enclosing rectangle of minimum area (but with no boundaries on the enclosing rectangle's width or height) has an ...

  4. Paper bag problem - Wikipedia

    en.wikipedia.org/wiki/Paper_bag_problem

    A cushion filled with stuffing. In geometry, the paper bag problem or teabag problem is to calculate the maximum possible inflated volume of an initially flat sealed rectangular bag which has the same shape as a cushion or pillow, made out of two pieces of material which can bend but not stretch.

  5. Cavalieri's principle - Wikipedia

    en.wikipedia.org/wiki/Cavalieri's_principle

    The volume ratio is maintained when the height is scaled to h' = r √ π. 3. Decompose it into thin slices. 4. Using Cavalieri's principle, reshape each slice into a square of the same area. 5. The pyramid is replicated twice. 6. Combining them into a cube shows that the volume ratio is 1:3.

  6. Finite volume method for two dimensional diffusion problem

    en.wikipedia.org/wiki/Finite_volume_method_for...

    The face areas in y two dimensional case are : = = and = =. We obtain the distribution of the property i.e. a given two dimensional situation by writing discretized equations of the form of equation (3) at each grid node of the subdivided domain.

  7. 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":

  8. Square–cube law - Wikipedia

    en.wikipedia.org/wiki/Square–cube_law

    Its volume would be multiplied by the cube of 2 and become 8 m 3. The original cube (1 m sides) has a surface area to volume ratio of 6:1. The larger (2 m sides) cube has a surface area to volume ratio of (24/8) 3:1. As the dimensions increase, the volume will continue to grow faster than the surface area. Thus the square–cube law.

  9. 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