09-23-2021-0734 - orthogonal instruction set

 In computer engineering, an orthogonal instruction set is an instruction set architecture where all instruction types can use all addressing modes. It is "orthogonal" in the sense that the instruction type and the addressing mode vary independently. An orthogonal instruction set does not impose a limitation that requires a certain instruction to use a specific register^[1] so there is little overlapping of instruction functionality.^[2]

Orthogonality was considered a major goal for processor designers in the 1970s, and the VAX-11 is often used as the benchmark for this concept. However, the introduction of RISC design philosophies in the 1980s significantly reversed the trend against more orthogonality. Modern CPUs often simulate orthogonality in a pre-processing step before performing the actual tasks in a RISC-like core.

https://en.wikipedia.org/wiki/Orthogonal_instruction_set

Straightedge and compass construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses.

The idealized ruler, known as a straightedge, is assumed to be infinite in length, have only one edge, and no markings on it. The compass is assumed to have no maximum or minimum radius, and is assumed to "collapse" when lifted from the page, so may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with collapsing compass; see compass equivalence theorem. Note however that whilst a non-collapsing compass held against a straightedge might seem to be equivalent to marking it, the neusis construction is still impermissible and this is what unmarked really means: see Markable rulers below.) More formally, the only permissible constructions are those granted by Euclid's first three postulates.

It turns out to be the case that every point constructible using straightedge and compass may also be constructed using compass alone, or by straightedge alone if given a single circle and its center.

The ancient Greek mathematicians first conceived straightedge and compass constructions, and a number of ancient problems in plane geometry impose this restriction. The ancient Greeks developed many constructions, but in some cases were unable to do so. Gauss showed that some polygons are constructible but that most are not. Some of the most famous straightedge and compass problems were proven impossible by Pierre Wantzel in 1837, using the mathematical theory of fields.

In spite of existing proofs of impossibility, some persist in trying to solve these problems.^[1] Many of these problems are easily solvable provided that other geometric transformations are allowed: for example, doubling the cube is possible using geometric constructions, but not possible using straightedge and compass alone.

In terms of algebra, a length is constructible if and only if it represents a constructible number, and an angle is constructible if and only if its cosine is a constructible number. A number is constructible if and only if it can be written using the four basic arithmetic operations and the extraction of square roots but of no higher-order roots.

Creating a regular hexagon with a straightedge and compass

https://en.wikipedia.org/wiki/Straightedge_and_compass_construction

https://en.wikipedia.org/wiki/Orthogonal_trajectory

https://en.wikipedia.org/wiki/Category:Curves

https://en.wikipedia.org/wiki/Category:Spherical_curves

https://en.wikipedia.org/wiki/Category:Splines_(mathematics)

https://en.wikipedia.org/wiki/Category:Spirals

https://en.wikipedia.org/wiki/Category:Roulettes_(curve)

https://en.wikipedia.org/wiki/Category:Helices

https://en.wikipedia.org/wiki/N-curve

https://en.wikipedia.org/wiki/Negative_pedal_curve

https://en.wikipedia.org/wiki/Asymptotic_curve

https://en.wikipedia.org/wiki/Center_of_curvature

https://en.wikipedia.org/wiki/Parallel_curve

https://en.wikipedia.org/wiki/Quadratrix

https://en.wikipedia.org/wiki/Equichordal_point

https://en.wikipedia.org/wiki/Free-form_deformation

https://en.wikipedia.org/wiki/French_curve

https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid

https://en.wikipedia.org/wiki/Ground_track

https://en.wikipedia.org/wiki/Sectrix_of_Maclaurin

https://en.wikipedia.org/wiki/Sierpiński_carpet

https://en.wikipedia.org/wiki/Spirograph

https://en.wikipedia.org/wiki/Strophoid

https://en.wikipedia.org/wiki/Subtangent

https://en.wikipedia.org/wiki/Superformula

https://en.wikipedia.org/wiki/Hemihelix

https://en.wikipedia.org/wiki/Space_cardioid

https://en.wikipedia.org/wiki/Horosphere

https://en.wikipedia.org/wiki/Horopter

https://en.wikipedia.org/wiki/Hypercycle_(geometry)

https://en.wikipedia.org/wiki/Implicit_curve

https://en.wikipedia.org/wiki/Inflection_point

https://en.wikipedia.org/wiki/Intersection_curve

https://en.wikipedia.org/wiki/Intrinsic_equation

https://en.wikipedia.org/wiki/Variation_diminishing_property

https://en.wikipedia.org/wiki/Vertex_(curve)

https://en.wikipedia.org/wiki/Trisectrix

https://en.wikipedia.org/wiki/Transcendental_curve

https://en.wikipedia.org/wiki/Triple_helix

https://en.wikipedia.org/wiki/Tendril_perversion

https://en.wikipedia.org/wiki/Torsion_of_a_curve

https://en.wikipedia.org/wiki/Tortuosity

https://en.wikipedia.org/wiki/Truncus_(mathematics)