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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
DefinitionSource checked

Direct and inverse proportion

Mathematics & logic

Constant-ratio and constant-product relationships.

Key knowledge

For positive x and y, direct proportion means y=kx with fixed k>0, so y/x stays constant. Inverse proportion means y=k/x, so xy stays constant. The constants in the two relationships are separately defined.

Values and equations

direct: y=k_d x; inverse: y=k_i/x

x, y
Positive variables declared quantity units
k_d
Fixed positive direct-proportion constant y-unit/x-unit
k_i
Fixed positive inverse-proportion constant x-unit·y-unit

Conditions and scope

  • The same constant must apply throughout the stated domain, with other influences held fixed.
  • State the units: a direct-proportion constant has y-units per x-unit, while an inverse-proportion constant has their product.
Sources · 2

References

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

  1. TIMES M35: ProportionAustralian Mathematical Sciences InstituteCourse notesamsi.org.auRead source
  2. Mathematics Exemplar · Direct and inverse proportionsNCERTTextbook chapter · PDFncert.nic.inRead source

Evidence and review

Constant-ratio and constant-product 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

Agreement within this scope

Positive direct proportion has constant ratio; inverse proportion has constant product.

The source ratio x/y uses the reciprocal of the constant in repository y=kx.

Entry detailsPermanent link to this entry ↗
Record identity
foundation-math-direct-inverse-proportion
Revision
foundations-audit.1
Structured reference record
Foundational core completion