Triangle median

Two or more lines are concurrent if there is a single point which lies on all of them. The three altitudes of a triangle (if taken as lines, not segments) are always concurrent, and their point of concurrency is called the orthocenter. The angle bisectors of a triangle are concurrent at a point equidistant from their sides, and the medians are concurrent two thirds of the way along each median from the vertex to the opposite side. The point of concurrency of the medians is the centroid. 

Consider the group element which rotates the molecule about a median of the central triangle. It interchanges the hydrogen locations in pairs, leaves one carbon location fixed, and interchanges the other two. Hence for this group element we write down the monomial write down, for the whole group,... 

Figure 1.62. Location of epithermal-type deposits in Japan (Shikazono and Shimizu, 1988a). 1 Green tuff and subaerial volcanic region of Tertiary/Quaternary ages, 2 Main Paleozoic/Mesozoic sedimentary terranes, 3 Main metamorphic terranes. TTL Tanakura tectonic line, ISTL Itoigawa-Shizuoka tectonic line, MTL Median tectonic line. Open circle epithermal Au-Ag vein-type deposits, solid circle epithermal base metal vein-type deposits, open triangle epithermal Au disseminated-type deposits.

Fig. 2.36. Tectonic setting of Kyushu, Japan, showing location of (north) Hishikari and Nansatsu (south) deposits in Kirishima arc. Triangle volcanoes younger than Middle Pleistocene stipple accretionary prism of Cretaceous and Tertiary age W-B zone isobath of deep Wadati-Benioff seismic zone MTL Median Tectonic Line BTL Butsuzo Tectonic Line K-P Ridge Kyushu-Palau Ridge (Mitchell and Leach, 1991).

In 2002, the Association of University Research Parks (AURP) contracted with Association Research Inc. (ARI) to develop a profile of US and Canadian Research Parks [6]. The ARI sent out questionnaires to 195 entities believed to be operating in research parks and received 87 written responses with 79 yielding sufficient information to be stored in a database. Research parks such as the Research Triangle Park occupy vast tracks of land (7000 acres), while others such as the University City Science Center (16 acres) and Audubon (3 acres) are relatively compact. The average size of a research park in the survey was 628 acres and the median 180 acres. Employment ranged from 10000 to 42 000 for 62 research parks. 

Figure 12. Comparison of normalized isotopic composition of weighted means versus elevation of Bolivian stations from Gonfiantini et al. (2001) for 1983 (triangles), 1984 (squares), and 1982 to 1986 averages (filled circles), and normalized 5180sw from small tributaries from Garzione et al. (2007) plotted at sample elevations. Model curves are weighted mean (bold), median (fine), la (coarse dashed), and 2a (fine dashed). Note that detailed location data needed to compute various hypsometric weighted means as discussed below are not yet published for these surface waters.

The center of mass of a figure. The centroid of a triangle is the intersection of the medians. 

The median of a triangle is the line from a vertex to the midpoint of the opposite side. 

Reflection of a median of a triangle about the corresponding angle bisector. 

The median elemental compositions of FAs, HAs, and NOM are rather similar, and so consequently are properties such as the average oxidation state of organic carbon and the total unsaturation of these materials. Most of the elemental compositions that were included in this review lie outside the biomass triangle on a van Krevelen plot, indicating that DOM is not simply a residue of biomass. It has clearly gained oxygen and lost hydrogen, as would be expected for partial oxidation of biomass to CO2 and H2O. 

Although a three-dimensional method of representation is necessary in order to give a complete picture of the isothermal conditions in a quaternary system, it is very convenient, for practical purposes, to make use of a plane diagram. Such a diagram can be obtained by projecting the curves in Fig. 143 perpendicularly on the base of the tetrahedron. The vertex of the tetrahedron (D) then comes to lie at the centre D of the triangle ABC (Fig. 144), and the edges AD, BD, and CD find their projections in the three medians AD, BD, and CD. 

Fig. 5.21. ExcitabUity in the three-variable system (5.1). The trajectory followed by this system in the conditions of fig. 5.18 is projected (dashed line) onto the plane (a, y) the corresponding evolution of )3 is represented in the inset. Shown as a function of the position of the steady state (filled circles) is the initial value of y (filled triangles) that must be exceeded to obtain the pulsatory amplification of the perturbation. The locus of these threshold values represents the threshold separatrix (Fitzhugh, 1961) whose position is close to the median branch of the product nullcline in the two-variable system (fig. 5.20) (Goldbeter etal, 1978).

W. Imrich, S. Klavzar, and H. M. Mnlder, Median graphs and triangle-free graphs, SIAMJ. Discrete Math. 12 (1999) 111-118. 

HF lies along the extension of a median of the cyclopropane equilateral triangle... 

Figure 1.18 (a) Time dependence of the drop concentration for OfW emulsions containing 0.02 wt% hydrocarbon in a 2 wt% Tween 20 aqueous phase at 50 C Filled symbols are for alkanes, unfilled symbols are for alkenes, of chain length given. (b) Time dependence of the median drop diameter for the same emulsions as in (a). Circles—Cu, squares—Cn. triangles—C,g filled—alkanes, unfilled— alkenes... 

---