{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.angular-measure","code":"thing-q1357788","url":"https://ver.cy/models/thing/q1357788/","name":"angular measure","alternateNames":["phase angle","angular displacement","angular difference","initial phase","Bragg angle","scattering angle","polar angle","angle between two vectors","angle of internal friction","phase angle of voltage","phase angle of electric current","grazing angle"],"kind":"thing","status":"published","version":"0.2.0-wave.1","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A measure of the size of an angle or of a rotation, expressed in units such as the radian (the SI unit), degree, gradian, turn and arcminute or arcsecond; a full turn equals 360 degrees or 2 pi radians, and related quantities include phase angle and angular displacement.","purpose":"Let an agent explain angular measures by unit, conversion, measurement and application in mathematics, physics, navigation and astronomy.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Measures rotation or opening","Radian is dimensionless in SI","Many units","Used across sciences"],"structure":{"bundles":[{"id":"units","name":"Units","description":"Which unit.","layers":[{"id":"convert","name":"Convert","description":"Conversion.","findings":[{"id":"convert-finding","name":"Convert","description":"Conversion.","questions":[{"text":"What is this angle in radians or degrees?","kind":"measurement"},{"text":"How precise must it be?","kind":"boundary"}]}]},{"id":"small","name":"Small angles","description":"Arcminutes and arcseconds.","findings":[{"id":"small-finding","name":"Small angles","description":"Small angles.","questions":[{"text":"How are arcminutes and arcseconds used?","kind":"definition"},{"text":"What is this in decimal degrees?","kind":"measurement"}]}]}]},{"id":"measure","name":"Measure","description":"Instruments.","layers":[{"id":"instrument","name":"Instrument","description":"Tools.","findings":[{"id":"instrument-finding","name":"Instrument","description":"Instruments.","questions":[{"text":"Which instrument measures this angle to the required accuracy?","kind":"provenance"},{"text":"How is it calibrated?","kind":"provenance"}]}]},{"id":"convention","name":"Convention","description":"Direction and sign.","findings":[{"id":"convention-finding","name":"Convention","description":"Conventions.","questions":[{"text":"Is the angle measured clockwise or anticlockwise, and from which reference?","kind":"definition"},{"text":"How are negative angles treated?","kind":"definition"}]}]}]},{"id":"mathematics","name":"Mathematics","description":"Trigonometry.","layers":[{"id":"trig","name":"Trigonometry","description":"Functions.","findings":[{"id":"trig-finding","name":"Trigonometry","description":"Trigonometry.","questions":[{"text":"What are the sine, cosine and tangent of this angle?","kind":"measurement"},{"text":"Is the calculator in degree or radian mode?","kind":"boundary"}]}]},{"id":"radian","name":"Radian","description":"Why radians.","findings":[{"id":"radian-finding","name":"Radian","description":"Radians.","questions":[{"text":"Why are radians natural in calculus?","kind":"definition"},{"text":"How is a radian defined?","kind":"definition"}]}]}]},{"id":"applications","name":"Applications","description":"Uses.","layers":[{"id":"navigation","name":"Navigation","description":"Bearings.","findings":[{"id":"navigation-finding","name":"Navigation","description":"Bearings.","questions":[{"text":"How are bearings expressed in navigation?","kind":"definition"},{"text":"What is the difference between true and magnetic bearings?","kind":"definition"}]}]},{"id":"astronomy","name":"Astronomy","description":"Angular size.","findings":[{"id":"astronomy-finding","name":"Astronomy","description":"Angular size.","questions":[{"text":"What is the angular size of this object in the sky?","kind":"measurement"},{"text":"How does it relate to distance and size?","kind":"definition"}]}]}]}]},"agentConduct":{"may":["Convert and report angles between units with stated precision.","Check that angular inputs to calculations use the expected unit."],"mustNot":["Mix degrees and radians silently in calculations that control machines or navigation.","Round angles in a way that hides errors relevant to safety.","Present an angle without its unit where it could be misread."],"requiresHuman":["Changing angular settings on machinery, antennas or vehicles that people rely on."]},"ethics":{"considerations":["Unit confusion in angles has caused failures in engineering and navigation.","Shared units let people across fields and countries check each other's work."],"affectedParties":["Engineers and navigators","People relying on systems built with these measures"]},"owners":{"steward":"Nobody owns it; the international metrology bodies define the SI unit.","roles":[],"masterSystems":[]},"relations":[{"target":"Q121960184","type":"parent","note":"registry parent class"},{"target":"Q123410660","type":"parent","note":"registry parent class"},{"target":"geometric measure","type":"related","note":"category"},{"target":"radian","type":"related","note":"unit"},{"target":"trigonometry","type":"related","note":"field"},{"target":"protractor and theodolite","type":"related","note":"instrument"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.angular-measure","Wikidata: Q1357788 (https://www.wikidata.org/wiki/Q1357788)","SI unit: radian (rad) plane angle"]},"properties":{"applicability":"not-applicable","items":["full turn: 360 or 2 pi degrees or rad - exact"]},"recognition":{"applicability":"optional","items":["Symbols such as deg, rad and arcsec","Protractors and theodolites","Slope as a percentage is a different measure","Not physical; shown on protractors, dials, compasses and in formulas."]},"capabilities":{"applicability":"required","items":["convert between degrees, radians and other units","measure angles with instruments","use angles in trigonometry and physics","read angular sizes in astronomy"]},"hazards":{"applicability":"required","items":["Mixing degrees and radians in calculations","Sign and direction conventions"]},"interfaces":{"applicability":"required","items":["SI Brochure (BIPM)","ISO 80000-3 space and time quantities"]},"context":{"applicability":"required","items":["Describing angles and rotations.","plane angles","solid angles (steradian)","phase angles","angular displacement","angles of scattering and diffraction"]}},"sources":[{"title":"Wikidata item Q1357788: angular measure","url":"https://www.wikidata.org/wiki/Q1357788","note":"identity and sense of the item"},{"title":"Wikipedia: Angular distance","url":"https://en.wikipedia.org/wiki/Angular_distance","note":"general description of the item"}],"openQuestions":["Should units be separate entries?","How should solid angle be linked?","How should navigation bearings be linked?"],"resources":{"spec":"/models/things/publications/thing-q1357788/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q1357788/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-11T12:56:33Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-06T19:51:54+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}