Isometreg

Mewn mathemateg, mae isometreg yn drawsffurfiad lle cedwir yr hyd (neu'r pellter) rhwng y gofod metrig heb ei newid.^[1] Mewn geiriau eraill, mae isometreg yn drawsffurfiad sy'n mapio elfennau o un gofod metrig i un arall, gan barchu hyd y gofod a geir rhwng yr elfennau, yn union. Mewn gofod Euclidaidd 2 a 3 dimensiwn, os yw dau ffigur (neu ddau siâp) yn perthyn i'w gilydd drwy isometreg, yna dywedir eu bod "yn gyfath". Mae'r berthynas hon, sy'n eu cysylltu, naill ai'n symudiad anhyblyg, neu'n adlewyrchiad.^[2]

Mae'r gair Groegaidd isos yn golygu "hafal", sy'n cyfeirio at y pellter rhwng yr elfennau.

↑ Coxeter 1969, t. 29
"We shall find it convenient to use the word transformation in the special sense of a one-to-one correspondence $P\to P'$ among all points in the plane (or in space), that is, a rule for associating pairs of points, with the understanding that each pair has a first member $P$ and a second member $P'$ and that every point occurs as the first member of just one pair and also as the second member of just one pair...
In particular, an isometry (or "congruent transformation," or "congruence") is a transformation which preserves length..."
↑ Coxeter 1969, t. 39
3.11 Any two congruent triangles are related by a unique isometry.

[CoxeterIsometryDef-1] Coxeter 1969, t. 29
"We shall find it convenient to use the word transformation in the special sense of a one-to-one correspondence $P\to P'$ among all points in the plane (or in space), that is, a rule for associating pairs of points, with the understanding that each pair has a first member $P$ and a second member $P'$ and that every point occurs as the first member of just one pair and also as the second member of just one pair...
In particular, an isometry (or "congruent transformation," or "congruence") is a transformation which preserves length..."

[2] Coxeter 1969, t. 39
3.11 Any two congruent triangles are related by a unique isometry.

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Isometreg

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