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Indirection
Published in Stephen Hester, David Francis, Eric Livingston, Ethnographies of Reason, 2016
Stephen Hester, David Francis, Eric Livingston
In the literature about mathematics, the central focus is often on individual proofs. In contrast, theorem provers are engaged in the work of proving theorems in the plural. To keep their place in that work, various “conventions” are maintained (although they can change and can, to varying degrees, be idiosyncratic). This stability of notation through and between courses of proving are important to discovery work.4 If a triangle ΔEFG is shown to be congruent to another triangle ΔABC, the ordering of the vertices in ΔEFG identifies the correspondence between the triangles. If ÐBAD is used to identify one of a pair of congruent angles, as in Figures 6 and 7, ÐCAD is used to identify the other, not ÐDAC. If a computation of area is written area(ΔABD) = ½·DF·AB, the same calculation doesn’t appear elsewhere as area(ΔABD) = ½·BA·FD. If a course of proving involves “cevians” (line segments between the vertices of a triangle and the sides opposite to them), a convention such as that shown in Figure 8 is used consistently. More generally, a host of more or less standard notations may be maintained—e.g., A, B, C for vertices or the angles of a trianglea, b, c for sides opposite the corresponding anglesha, hb, hc for the altitudes upon a, b, c.ta, tb, tc, for the internal bisectors of A, B, Cta’, tb’, tc’, for the external bisectors of A, B, CA’, B’, C’ for the midpoints of a, b, cma, mb, mc for the medians to a, b, cO for the circumcenter, I for the incenter, H for the orthocenter, and G for the centroid of a triangle
A hybrid approach of fuzzy risk assessment-based incenter of centroid and MCDM methods for multimodal transportation route selection
Published in Cogent Engineering, 2022
Nitidetch Koohathongsumrit, Wasana Chankham
Assuming be the balancing point generated from the coordination of Q1, Q2, and Q3. Then, the incenter of centroid point is determined as follows: