was possible to build a 500-story tower to provide affordable office space for this densely packed city, but with the danger to buildings from earthquakes, architects considered that a triangular shape would be necessary if such a building were to be built. In New York City, as Broadway crisscrosses major avenues, the resulting blocks are cut like triangles, and buildings have been built on these shapes; one such building is the triangularly shaped Flatiron Building which real estate people admit has a "warren of awkward spaces that do not easily accommodate modern office furniture" but that has not prevented the structure from becoming a landmark icon. Designers have made houses in Norway using triangular themes. Triangle shapes have appeared in churches as well as public buildings including colleges as well as supports for innovative home designs. Triangles are sturdy; while a rectangle can collapse into a parallelogram from pressure to one of its points, triangles have a natural strength which supports structures against lateral pressures. A triangle will not change shape unless its sides are bent or extended or broken or if its joints break; in essence, each of the three sides supports the other two. A rectangle, in contrast, is more dependent on the strength of its joints in a structural sense. Some innovative designers have proposed making bricks not out of rectangles, but with triangular shapes which can be combined in three dimensions. It is likely that triangles will be used increasingly in new ways as architecture increases in complexity. It is important to remember that triangles are strong in terms of rigidity, but while packed in a tessellating arrangement triangles are not as strong as hexagons under compression (hence the prevalence of hexagonal forms in nature). Tessellated triangles still maintain superior strength for cantilevering however, and this is the basis for one of the strongest man made structures, the tetrahedral truss. See also Apollonius' theorem Congruence (geometry) Desargues' theorem Dragon's Eye (symbol) Fermat point Hadwiger–Finsler inequality Heronian triangle Integer triangle Law of cosines Law of sines Law of tangents Lester's theorem List of triangle inequalities List of triangle topics Modern triangle geometry Ono's inequality Pedal triangle Pedoe's inequality Pythagorean theorem Special right triangles Triangle center Triangular number Triangulated category Triangulation (topology) Notes References External links Clark Kimberling: Encyclopedia of triangle centers. Lists some 5200 interesting points associated with any triangle.