Pith Number

pith:YWDNEJHL

pith:2026:YWDNEJHLGDZCN7BSXYV4BB7LDO

not attested not anchored not stored refs resolved

An optimization problem for triangles

Kevin Tran, Tommy Murphy

Optimizing the product of distances from an interior point to a triangle's vertices falls into one of two cases, fully specified for isosceles triangles.

arxiv:2605.12985 v1 · 2026-05-13 · math.MG

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\pithnumber{YWDNEJHLGDZCN7BSXYV4BB7LDO}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

For isosceles triangles, we explicitly show exactly when both cases occur.

C2weakest assumption

The optimization problem admits exactly two possible cases in general.

C3one line summary

Optimizing the product of distances from a point to a triangle's vertices has two cases, resolved explicitly for isosceles triangles.

References

6 extracted · 6 resolved · 0 Pith anchors

[1] Kimberling, C.Central Points and Central Lines in the Plane of a TriangleMath. Mag. 67 (1994), no. 3, 163–187 1994

[2] and Robbins, H.What Is Mathematics?, 2nd ed 1941

[3] Hajja, M.An Advanced Calculus Approach to Finding the Fermat Point, Math. Mag., Vol. 67 (1994), no. 1, 29–34 1994

[4] Problems, Hints and Solutions, unpublished 1988

[5] A.,Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle, Boston, MA: Houghton Mifflin, pp

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-18T03:09:00.616640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c586d224eb30f226fc32be2bc087eb1babfea420912d681ba031fba1b1b2bf1d

Aliases

arxiv: 2605.12985 · arxiv_version: 2605.12985v1 · doi: 10.48550/arxiv.2605.12985 · pith_short_12: YWDNEJHLGDZC · pith_short_16: YWDNEJHLGDZCN7BS · pith_short_8: YWDNEJHL

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YWDNEJHLGDZCN7BSXYV4BB7LDO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c586d224eb30f226fc32be2bc087eb1babfea420912d681ba031fba1b1b2bf1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1112d8d1ac9af6f3765e78921c80edb3cc014cf626c22c4f4eec9a81d3969f61",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-05-13T04:32:48Z",
    "title_canon_sha256": "514a0c17d89e64e1c1ad3bef25b2a347ae6d3adb6bdf9c1b20367908533d936c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12985",
    "kind": "arxiv",
    "version": 1
  }
}