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Showing 1621–1650 of 1709 reference entries

Chemistry · PhysicsIntensive, extensive, specific and molar properties

Scaling the system amount is different from changing its state.

Definition
Chemistry · MeasurementRelative atomic mass and isotope composition

Relative atomic mass is dimensionless and depends on the isotope composition being averaged.

Definition
Chemistry · MeasurementMolar mass and mass–amount conversion

Molar mass converts a specified substance's amount into mass.

Definition
Chemistry · MeasurementAmount concentration, molality and composition fractions

Concentration must declare its numerator and denominator.

Definition
ChemistryDilution conserves the retained solute amount

Dilution arithmetic refers to final solution volume, not the amount of solvent poured in.

Method
ChemistryLimiting reagent, theoretical yield and percent yield

Stoichiometry gives a maximum under a specified reaction model; recovery measures the actual yield.

Method
ChemistryFormal charge is equal-share electron accounting

Formal charge, oxidation state and partial charge answer different questions.

Definition
ChemistryElectrolyte strength, solubility and concentration

Strong describes ion formation by dissolved solute, not how much solute dissolves.

Definition
ChemistryComplete ionic and net ionic equations

Cancel unchanged species while conserving both atoms and charge.

Method
Biology · ChemistryWater polarity and biological interactions

Water's molecular interactions help explain solvation, cohesion and thermal buffering.

Empirical finding
BiologyCell size and surface-to-volume scaling

For geometrically similar cells, volume grows faster than surface area.

Model
Biology · ChemistryOsmolarity and tonicity

Total particle concentration and lasting cell-volume effect are different properties.

Definition
BiologyChromosome sets and DNA content

DNA replication doubles DNA content without doubling chromosome-set ploidy.

Definition
BiologyOrganisms, populations, communities and ecosystems

Ecological levels describe different interacting sets and environments.

Definition
BiologyPopulation size, density and demographic balance

Total individuals and individuals per area or volume must be distinguished.

Model
BiologyMutation and selection: different roles

Mutations do not generally appear because an organism needs their future advantage.

Empirical finding
BiologyClades and rooted-tree interpretation

Shared ancestry is represented by topology, not by the left-to-right order of tips.

Method
Biology · ChemistryPlant water potential and pressure balance

Osmotic and mechanical contributions together determine passive water movement.

Model
Earth & cosmosRock and mineral are different material categories

A mineral species and a rock aggregate have different identifying features.

Definition
Earth & cosmosEarth's compositional and mechanical layers

Crust–mantle–core and lithosphere–asthenosphere partition Earth by different properties.

Model
Earth & cosmos · MeasurementGeodetic latitude, longitude and reference systems

A coordinate pair needs a reference surface, origin and convention.

Definition
Earth & cosmos · MeasurementMap projections and distortion

Flattening Earth's curved reference surface requires a choice of distortions.

Model
Earth & cosmos · MeasurementEllipsoid height, geoid and orthometric height

Height above a geometric reference is not automatically height above a gravity reference.

Definition
Earth & cosmosRotation, axial tilt and seasonal sunlight

Axial tilt changes the angle and duration of sunlight in opposite hemispheres.

Model
Earth & cosmosNatural hazard and disaster risk

A harmful physical process and the potential losses it creates are different quantities.

Definition
Earth & cosmosUsing present processes to infer Earth's past

Modern process evidence informs geological interpretation only with the past boundary conditions.

Method
Earth & cosmosLunar phases and synchronous rotation

Phases change the visible illuminated fraction; they are not Earth's shadow moving across the Moon.

Model
Earth & cosmosSolar and lunar eclipse geometry

New or full Moon is necessary for the corresponding eclipse but does not guarantee alignment.

Model
Earth & cosmosIAU Solar-System body categories

A scoped naming convention distinguishes planets, dwarf planets, small bodies and satellites.

Definition
Earth & cosmos · MeasurementAstronomical unit and light-year

The astronomical unit and light-year measure lengths, with different defining conventions.

Definition
ModelSource checked

Map projections and distortion

Earth & cosmosMeasurement

Flattening Earth's curved reference surface requires a choice of distortions.

Key knowledge

A map projection assigns positions on a curved Earth reference surface to a plane. Over finite curved regions, a flat map cannot preserve every distance, area, shape and direction simultaneously. Equal-area, conformal and equidistant projections preserve different specified properties; equidistant does not mean that every pair of mapped points has its true distance.

Conditions and scope

  • Select a projection and scale appropriate to the region and measurement; local small-area errors may be small even when global distortion is large.
  • Projection properties apply to the chosen reference surface and parameters. A projection alone does not specify or transform the underlying geodetic datum.
Sources · 3

References

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

  1. GEOG 486, Projection properties: Equivalent, Conformal and EquidistantCary Anderson and Fritz Kessler · Penn StateTextbook chaptercourses.ems.psu.eduRead source
  2. How are different map projections used?U.S. Geological SurveyReference guideusgs.govRead source
  3. A Guide to Coordinate Systems in Great Britain, v3.6 (2020), §§1.2 and 3.1Ordnance SurveyReference guide · PDFordnancesurvey.co.ukRead source

Evidence and review

Directly inspected Penn State's opening and Equivalent, Conformal and Equidistant bodies on distortion, local angles, area–shape tradeoffs and distance preservation only from specified points or lines. Also read the indexed complete USGS FAQ answer; direct HTML extraction did not expose it and the poster PDF returned 403. OS coordinate-system distinctions constrain the datum clause. Excludes the FAQ's overbroad 'only Mercator' direction wording and a spherical great-circle shortcut for all ellipsoidal geodesics.

2026-10-10 · Independent Mathematics and Information editor (/root/core_math_information). Independent AI editorial review of this entry's statements, equations, applicability conditions and source coverage. Source checks apply to these claims within their stated limits.

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