Description
Return their ratio and vertexToCentroid-2 × centroidToMidpoint as twoToOneResidual.
Triangle identities relate side lengths, angles, and special points under a nondegenerate geometric model. A contribution to a point or a local ratio is different from constructing the complete point or proving that supplied values form a triangle.
Return their ratio and vertexToCentroid-2 × centroidToMidpoint as twoToOneResidual.
When to use this tool
Use Triangle Median Ratio when you need an explicit triangle identity or local construction.
How to use the tool and how it works
- Enter vertexToCentroid, centroidToMidpoint. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read ratio, twoToOneResidual. Use the output convention below.
Require nonnegative vertexToCentroid and positive centroidToMidpoint. Return their ratio and vertexToCentroid-2 × centroidToMidpoint as twoToOneResidual.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vertexToCentroid | Vertex To Centroid | Required. Finite number; minimum 0. |
| centroidToMidpoint | Centroid To Midpoint | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| ratio | Dimensionless ratio under the numerator/denominator convention above. | Required. Finite number. |
| twoToOneResidual | Two To One Residual | Required. Finite number. |
{
"input": {
"vertexToCentroid": 8,
"centroidToMidpoint": 4
},
"output": {
"ratio": 2,
"twoToOneResidual": 0
}
}Limitations and assumptions
- Both lengths share units; this checks supplied median segments without locating a centroid, validating a triangle, or proving the measured point is its centroid.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Construct the triangle from coordinates or solve the complete geometric constraints when consistency matters. Match side ordering, angle units, and internal-versus-external conventions to the intended identity.
References
Similar or alternative tools
- Triangle Isogonal Cevian Ratio
Return (adjacentFirst/adjacentSecond)²/firstRatio.
- Triangle Altitude Foot Parameter
Use scaled coordinates and a normalized B-to-C direction to project A onto its supporting line, returning parameter and foot coordinates.