GLOBAL KNOWLEDGE ARK

Reference library

Foundations

Explore concepts, laws, equations and methods, with clear explanations of their use and sources. Choose an area of study or find a specific entry.

More filters

Reference entries

Showing 1651–1680 of 1709 reference entries

Mathematics & logicOrder of arithmetic operations

Grouping and equal-priority arithmetic evaluation.

Method
Mathematics & logicScientific notation

A normalized decimal coefficient with an integer power of ten.

Definition
Mathematics & logicDirect and inverse proportion

Constant-ratio and constant-product relationships.

Definition
Mathematics & logicAngles, intersecting lines and parallel lines

Euclidean line-angle relationships.

Mathematical statement
Mathematics & logicAngle sums of polygons

Interior and exterior angle sums for convex polygons.

Mathematical statement
Mathematics & logicSine and cosine rules for triangles

Side-angle laws beyond right triangles.

Mathematical statement
Mathematics & logicPigeonhole principle

A finite assignment forces a shared output when inputs outnumber outputs.

Mathematical statement
Mathematics & logicTotal probability and event Bayes' theorem

Finite-partition probabilities and reversal of event conditioning.

Mathematical statement
Mathematics & logicLeast common multiple

The smallest positive common multiple of positive integers.

Definition
Mathematics & logicPolynomials and degree

Finite sums of nonnegative integer powers with fixed coefficients.

Definition
Mathematics & logicDecimal rounding and significant digits

Decimal places, retained significant digits and rounding ties.

Method
Mathematics & logicCone and sphere volume and surface area

Euclidean cone and sphere mensuration.

Mathematical statement
Mathematics & logicCircle angles and tangents

Inscribed angles and radius-tangent perpendicularity.

Mathematical statement
Mathematics & logicStraight-line equations

Slope-intercept form of a nonvertical line.

Mathematical statement
InformationProgram names, bindings and assignment

Names refer to values through an execution environment.

Definition
InformationSequence, conditionals and loops

Selection and repetition determine which program statements execute.

Definition
InformationFunction definitions, parameters and calls

A call connects arguments with local parameter bindings.

Definition
InformationRecursive procedures and base cases

Self-calls reduce a problem toward a terminating case.

Method
InformationData types and checking

Types describe values and permitted operations; checks occur at different stages.

Definition
InformationPrograms and processes

An operating system manages a program's execution as a process.

Definition
InformationVirtual address spaces

A process's address view is distinct from physical memory placement.

Definition
InformationFiles, directories and persistence

File contents, directory names and durable storage have distinct roles.

Definition
Mathematics & logicPolygon perimeter and parallel-base areas

Boundary length and enclosed area measure different properties of a plane shape.

Method
Physics · ChemistryOpen, closed, isolated and adiabatic systems

A system boundary determines which transfers count as exchanges.

Definition
PhysicsHypothesis, law and scientific theory

These terms name different scientific roles rather than steps in a promotion ladder.

Definition
PhysicsConduction, convection and thermal radiation

Heat can be transferred by microscopic interactions, fluid motion or electromagnetic radiation.

Definition
PhysicsConvective heat-transfer coefficient

The coefficient h represents a specified surface–fluid transfer situation.

Model
PhysicsLumped thermal relaxation and Biot criterion

An approximately uniform-temperature body can have an exponential thermal response.

Model
PhysicsNet radiation exchange and gray surfaces

Emission and absorption must both enter a net radiative heat balance.

Model
Measurement · PhysicsSolid angle and steradian

A solid angle measures a cone of directions rather than a plane rotation.

Definition
Mathematical statementSource checked

Angles, intersecting lines and parallel lines

Mathematics & logic

Euclidean line-angle relationships.

Key knowledge

Adjacent angles forming a straight angle sum to π radians; angles around a point sum to 2π. Vertically opposite angles are equal. A transversal crossing two parallel lines forms equal corresponding and alternate interior angles, with same-side interior angles summing to π.

Values and equations

linear pair: α+β=π; full turn: Σ_i θ_i=2π

α, β
Adjacent angles whose outer rays form a straight line rad
θ_i
Nonoverlapping successive angles making one complete turn rad
i
Finite angle index

Conditions and scope

  • Use distinct straight lines in one Euclidean plane and angles measured in a consistent convention.
  • For the parallel-line conclusions, the transversal meets the two lines at different points.
Sources · 2

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. Explanatory Notes to Junior Secondary Mathematics Curriculum (2020), learning units 19–20Education Bureau, Hong KongTeaching resource · PDFedb.gov.hkRead source
  2. TIMES · Introduction to plane geometryAMSI and University of Melbourne, ICE-EMTeaching resourceamsi.org.auRead source

Evidence and review

Euclidean line-angle relationships.

2026-10-10 · Independent Physics and Measurement reference editor (AI editorial bounded review). Exact bounded introductory reference claims and this practical concept inventory are approved after closure. Existing university/research proof and source scopes remain separate; no universal knowledge-completeness or experimental-validation assertion.

Foundational review

2026-10-10 · Independent AI editorial inspection of this new compact reference entry, its equations, applicability, sources and knowledge connections.

Sources from other places

Scope or convention differs

Euclidean straight/full turns, vertical angles and parallel-transversal angle relations.

The module expresses the same angle sizes in degrees, while the repository uses radians.

  • Australian Mathematical Sciences Institute and University of Melbourne

Entry detailsPermanent link to this entry ↗
Record identity
foundation-math-line-angle-relations
Revision
foundations-audit.1
Structured reference record
Foundational core completion