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A primitive Euler brick is an Euler brick whose edge lengths are relatively prime. A perfect Euler brick is one whose space diagonal is also an integer, but such a brick has not yet been found. Euler brick with edges a , b , c and face diagonals d , e , f
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A rectangular cuboid with integer edges, as well as integer face diagonals, is called an Euler brick; for example with sides 44, 117, and 240. A perfect cuboid is an Euler brick whose space diagonal is also an integer. It is currently unknown whether a perfect cuboid actually exists. [6]
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Many of these items named after Euler include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical entity. Many of these entities have been given simple yet ambiguous names such as Euler's function, Euler's equation, and Euler's formula.
Chapter 13 relates Pythagorean triangles to rational points on a unit circle, Chapter 14 discusses right triangles whose sides are unit fractions rather than integers, and Chapter 15 is about the Euler brick problem, a three-dimensional generalization of Pythagorean triangles, and related problems on integer-sided tetrahedra.
Fig. 2: Column effective length factors for Euler's critical load. In practical design, it is recommended to increase the factors as shown above. The following assumptions are made while deriving Euler's formula: [3] The material of the column is homogeneous and isotropic. The compressive load on the column is axial only.
Top: A failed attempt on a plane — the missed wall is indicated Bottom: A solution on a torus — the dotted line is on the back side of the torus Comparison of the graphs of the Seven bridges of Konigsberg (top) and Five-room puzzles (bottom).