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Versine: History & Applications

The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit Aryabhatiya, Section I) trigonometric tables. The versine of an angle is 1 minus its cosine.

Language: English [EN]
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Versine topic overview

The analysis highlights History and Applications as prominent areas in the source structure around Versine.

Related topics
67
Source areas
5
Connected nodes
72
Extracted relationships
27
Related term clusters
24
Bridge connections
72

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

History and applications · 44 topics
Arbitrary curves and chords · 10 topics
Overview · 9 topics
Approximations · 2 topics
Mathematical identities · 2 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

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Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

History and applications

Mathematical identities

Approximations

Arbitrary curves and chords

For the semantics nerds

You can skip this section if you’re here for content ideas and keyword inspiration.

Advanced semantic analysis

How Versine connects Entity context

The extracted context around Versine shows recurring relationship patterns in the source. For example, Versine → AB, AC, CD, Illustrated, OC, OD, Thus Another extracted example is Versine → AC, Alternatively, Chinese, Guo Shoujing, Shen Kuo. Use these groups to spot repeated connection types before inspecting the individual relationships.

Versine

Top relations

related to Versine and coversine · 7
Versine → AB, AC, CD, Illustrated, OC, OD, Thus
related to Approximations · 5
Versine → AC, Alternatively, Chinese, Guo Shoujing, Shen Kuo
related to Haversine · 5
Versine → Earth's, José, Mendoza, One, Ríos
related to Modern uses · 4
Versine → Hann, One, Poisson, Tukey
related to Arbitrary curves and chords · 3
Versine → Given, Hallade, L2
related to overview · 2
Versine → Expressed, In Latin
related to Inverse functions · 1
Versine → Inverse

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

haversine sine used also functions chord versin versed tables formula sagitta navigation trigonometric coversine zero displaystyle frac function latin one

Versine relationships Subject–Predicate–Object triples

TTTA extracted 27 structured relationships around Versine. Examples in this analysis include Versine → related to Approximations → AC and Versine → related to Approximations → Alternatively. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Versinerelated to ApproximationsAC0.60section
Versinerelated to ApproximationsAlternatively0.60section
Versinerelated to ApproximationsChinese0.60section
Versinerelated to ApproximationsShen Kuo0.60section
Versinerelated to ApproximationsGuo Shoujing0.60section
Versinerelated to Arbitrary curves and chordsGiven0.60section
Versinerelated to Arbitrary curves and chordsL20.60section
Versinerelated to Arbitrary curves and chordsHallade0.60section
Versinerelated to HaversineEarth's0.60section
Versinerelated to HaversineOne0.60section
Versinerelated to HaversineJosé0.60section
Versinerelated to HaversineMendoza0.60section

Related concept clusters Related term clusters

The concept neighborhoods around Versine bring nearby vocabulary together. In this analysis, examples include Used, Zero and Two. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • trigonometric function
    • Tables
    • Versed
    • Functions
    • Applications
    • Cosine
    • Earliest
    • Sine
    • Coversine
    • Function
    • Trigonometric
    • Versine
    • Versin
  • trigonometric tables
    • Tables
    • Trigonometric
    • Functions
    • Versed
    • Versine
    • Cosine
    • Versin
    • Earliest
    • Coversine
    • Function
    • Use
    • Zero
  • cosine
    • Trigonometric
    • Tables
    • Versin
    • Cos
    • Latin
    • Operatorname
    • Table
    • Terms
    • Theta
    • Two
    • Versine
    • Coversine
  • haversine formula
    • Navigation
    • Used
    • Versin
    • Radius
    • Also
    • Applications
    • Cos
    • Operatorname
    • Theta
    • Use
    • Displaystyle
    • Frac
  • trigonometric functions
    • Tables
    • Functions
    • Trigonometric
    • Versed
    • Cosine
    • Haversine
    • Earliest
    • Coversine
    • Function
    • Operatorname
    • Terms
    • Theta
  • sine
    • Versed
    • Versus
    • Earliest
    • Latin
    • Function
    • Trigonometric
    • Functions
    • Tables
    • Also
    • Haversine
    • Cos
    • Distance
  • logarithmic tables
    • Trigonometric
    • Versine
    • Versed
    • Versin
    • Cosine
    • Coversine
    • Use
    • Zero
    • Formula
    • Functions
    • Also
    • Used
  • half-angle formula
    • Navigation
    • Used
    • Versin
    • Radius
    • Cos
    • Operatorname
    • Theta
    • Displaystyle
    • Frac
    • Use
    • Haversine
    • Versine

Connections between topic areas Semantic bridges

For Versine, one of the stronger structural bridges in this analysis connects Versine with History and applications. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Versine — History and applications · splits 28 ⟂ 45
Versine — Arbitrary curves and chords · splits 62 ⟂ 11
Versine — Overview · splits 63 ⟂ 10
Versine — Mathematical identities · splits 70 ⟂ 3
Versine — Approximations · splits 70 ⟂ 3

Map overview Semantic statistics

Versine

Nodes73
Edges72
Triples27
Avg. degree1.97
Density0.027397
Components1

Source & methodology

TTTA analyzes the structure around Versine to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as History & Applications, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Versine · EN edition · Analysis: TopicsToTalkAbout

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