An Evolutionary Tree for Form
Our original mathematics were naturalistic, a product of sensory observation of environment.
Our current mathematical exploration is towards an optimized product out of our sensory observation of the environment.
Craft was the original term used to encompass the sensory observation.
Building was the developed form of the craft that allowed the creation of the skill of Chief Builder, ‘arkhitekton’.
Architecture is their craft, their sensory input and output skill.
Architecture is the ongoing optimization of the sensory observation in terms of its functional utility, its material stability and innovation in materials, and the art of assembly to produce a sensory feedback that is emotionally stimulating.
Form is the product of the use of Architectural semiosis.
Form, for any object, can be examined in terms of Evolutionary Tree relationships that may assist the designer in developing an optimized solution.
Evolutionary Tree Type 001 – Component development.
Coordinate (x,y,z) to line
Line to triangle
Triangle to scalene triangle as a randomizer of line and coordinate.
Triangle to isosceles triangle as a less random locator of line and coordinate.
Isosceles triangle to point on the circumference of a circle.
Triangle to curved equilateral triangle to sphere.
Triangle to fractal equilateral triangle to infinity.
Triangle to equilateral triangle to tetrahedron, octahedron, hexagon and icosahedron.
Triangle to right angle triangle to point on the circumference of a circle to a sphere
Triangle to right angle triangle to circle to nonagon, septagon, decagon, star polygon, decagram, petrie polygons and pentagon.
Triangle to square to rhombus to kite to quadrilateral to trapezoid to isosceles trapezoid
Triangle to square to rectangle to parallelogram to quadrilateral
Triangle to right angle triangle to square to Pythagorean Theorem to cuboid.
To right angle triangle to spiral to Fibonacci series to ratio to proportion to scale to dimension.
To right angle triangle to spiral to minimal surfaces to sphere to hemisphere to catenoid to torus to ring torus to spindle torus to horn torus to geodesic to helicoid to saddle to fractal form.
Form can also be examined in the sequence of compactness, area, perimeter, volume, and surface area.
This allows for form to be designed in the sequence of need, available site area, proposed or existing plan, section and envelope.
Evolutionary Tree Type 002 – 2D Compactness of a shape.
Square, circle, pentagon, polygons, equilateral triangle, rhombus, trapezoid, rectangle, kite, right angle triangle.
Evolutionary Tree Type 003 – 2D Form in order of magnitude of space used.
Isosceles triangle, right angle triangle, equilateral triangle, parallelogram, circle, square.
Evolutionary Tree Type 004 – 2D Form in order of magnitude of area for the same perimeter.
Circle, square, parallelogram, right angle triangle, isosceles triangle, equilateral triangle.
Evolutionary Tree Type 004 – 2D Form in order of magnitude of perimeter for the same area.
Equilateral triangle, isosceles triangle, right angle triangle, parallelogram, square, circle.
Evolutionary Tree Type 005 – 3D Form in magnitude of volume for the same plan area for each shape.
Cylinder, cube, prism, truncated cube variants, sphere, truncated cube, tetrahedron.
Evolutionary Tree Type 006 – 3D Form in order of magnitude of surface area for the same plan area for each shape.
Cylinder, prism, cube, cube variants, truncated cube, tetrahedron, sphere.
Evolutionary Tree Type 007 – 3D Form in order of minimum surface area for equal volumes for each shape.
Sphere, cylinder, cube, cone, pyramid.
Evolutionary Tree Type 008 – 3D Form in order of magnitude of surface area to volume for each shape.
Plane, tetrahedron, cube, octahedron, dodecahedron, icosahedron, sphere.
Evolutionary Tree Type 009 – 3D Form in order of magnitude of volume for each shape.
Sphere, icosahedron, dodecahedron, octahedron, cube, tetrahedron, plane.
The examination of each shape tree leads to the conclusion that the Form of a shape is independent of dimension.
Form is a characteristic of the complete shape itself and each shapes characteristics.
The most compact forms in two dimensions are squares, equilateral triangles and circles.
The most compact forms in three dimensions are tetrahedrons, pyramids, spheres and planes.
The ideal compact Form has minimal site area use, minimal volume, minimal surface area, minimal material use, minimal energy use, maximum passive energy use and minimal construction time.
Ian K Whittaker
Websites:
https://sites.google.com/site/architecturearticles
Email: iankwhittaker@gmail.com
01/07/2013
01/11/2013
14/10/2020
709 words over 3 pages