Everyone is en titled

 Everyone is en titled to their own title...the reality presented by all nuts is the brain like resemblance to said  eclectric moulded NaCl/H((2)) listening to EP Chapter three Occhams cake comes to mind as the one example which puts entrupy back down where it belings at the inverse end of 186 or the rounded version f(3χ6) ακα ΓοψκΥ where the edge will entropy itzelf back to the end and the end is the end of the end as energy is entered into the equation pointing to the point of the point which is the edge defined by the (())cc ηαμζ Γαζ()Γ the one process is the inverse of the other as are 66 degrees when subtended by 24 the angle of more spin with which the ryhme of the dime is the slime of time so please do try it at home and see that in both directions of entropy the edge of a blade will immediately begin to reverse itself at the speed of in verted version such as the Red Wood the Mountain the Sea ground a broken pane of glass back into sand using the force of friction convert more friction into flame melt said silicon into a wilicon window which only crashes when the foot is put through the screen in a uni of(verse) rather than at the random whim of the windoze wallet wiper...Billy the big thinker thinking the world into a smaller pile of things with all of the moon eye wallet lines linked to the wallet of he as we wait for him to turn back into silicon salted less by water than you and theee anyway the initial state of an edge is always predictable by looking at it and dropping a ripe tomato on the fine angled edge of to see where the angle lies relative to the right hand quadrant of the unit circle where the top semi chrome dome is A the left when looked at from the right is C the right when eyed from the left or the center is D and as the radian approaches ((18)) aka 3χ6 τηε εΔΓΣ ιΣΣ evident as is the D which the edge will return to as the at most of the sphere beats the blade back to the base of ace waiting for you the crafty cook to move the molecules around again re turning the blade into the leg of a chair or the cutter of hair

Of a triangle

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The centroid of a triangle is the point of intersection of its medians (the lines joining each vertex with the midpoint of the opposite side).^[4] The centroid divides each of the medians in the ratio 2:1, which is to say it is located ⅓ of the distance from each side to the opposite vertex (see figures at right).^[10][11] Its Cartesian coordinates are the means of the coordinates of the three vertices. That is, if the three vertices are ${\displaystyle L=(x_{L},y_{L}),}$ ${\displaystyle M=(x_{M},y_{M}),}$ and ${\displaystyle N=(x_{N},y_{N}),}$ then the centroid (denoted C here but most commonly denoted G in triangle geometry) is

$${\displaystyle C={\frac {1}{3}}(L+M+N)=\left({\frac {1}{3}}(x_{L}+x_{M}+x_{N}),\;\;{\frac {1}{3}}(y_{L}+y_{M}+y_{N})\right).}$$

The centroid is therefore at ${\displaystyle {\tfrac {1}{3}}:{\tfrac {1}{3}}:{\tfrac {1}{3}}}$ in barycentric coordinates.

In trilinear coordinates the centroid can be expressed in any of these equivalent ways in terms of the side lengths a, b, c and vertex angles L, M, N:^[12]

$${\displaystyle {\begin{aligned}C&={\frac {1}{a}}:{\frac {1}{b}}:{\frac {1}{c}}=bc:ca:ab=\csc L:\csc M:\csc N\\[6pt]&=\cos L+\cos M\cdot \cos N:\cos M+\cos N\cdot \cos L:\cos N+\cos L\cdot \cos M\\[6pt]&=\sec L+\sec M\cdot \sec N:\sec M+\sec N\cdot \sec L:\sec N+\sec L\cdot \sec M.\end{aligned}}}$$

The centroid is also the physical center of mass if the triangle is made from a uniform sheet of material; or if all the mass is concentrated at the three vertices, and evenly divided among them. On the other hand, if the mass is distributed along the triangle's perimeter, with uniform linear density, then the center of mass lies at the Spieker center (the incenter of the medial triangle), which does not (in general) coincide with the geometric centroid of the full triangle.

The area of the triangle is 1.5 times the length of any side times the perpendicular distance from the side to the centroid.^[13]

A triangle's centroid lies on its Euler line between its orthocenter H and its circumcenter O, exactly twice as close to the latter as to the former:^[14][15]

f(x)=χ/σιν(Χ) + 1/υ/σιν(υ)

f(χ:y)=χ/sin(χ) + 1/υ/sin(υ)

By lengths of sides

Ancient Greek mathematician Euclid defined three types of triangle according to the lengths of their sides:^[1][2]

Greek: τῶν δὲ τριπλεύρων σχημάτων ἰσόπλευρον μὲν τρίγωνόν ἐστι τὸ τὰς τρεῖς ἴσας ἔχον πλευράς, ἰσοσκελὲς δὲ τὸ τὰς δύο μόνας ἴσας ἔχον πλευράς, σκαληνὸν δὲ τὸ τὰς τρεῖς ἀνίσους ἔχον πλευράς, lit. 'Of trilateral figures, an isopleuron [equilateral] triangle is that which has its three sides equal, an isosceles that which has two of its sides alone equal, and a scalene that which has its three sides unequal.'^[3]

• An equilateral triangle (Greek: ἰσόπλευρον, romanized: isópleuron, lit. 'equal sides') has three sides of the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°.^[4]
• An isosceles triangle (Greek: ἰσοσκελὲς, romanized: isoskelés, lit. 'equal legs') has two sides of equal length.^{[note 1][5]} An isosceles triangle also has two angles of the same measure, namely the angles opposite to the two sides of the same length. This fact is the content of the isosceles triangle theorem, which was known by Euclid. Some mathematicians define an isosceles triangle to have exactly two equal sides, whereas others define an isosceles triangle as one with at least two equal sides.^[5] The latter definition would make all equilateral triangles isosceles triangles. The 45–45–90 right triangle, which appears in the tetrakis square tiling, is isosceles.
• A scalene triangle (Greek: σκαληνὸν, romanized: skalinón, lit. 'unequal') has all its sides of different lengths.^[6] Equivalently, it has all angles of different measure.

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  Equilateral Triangle

 
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  Isosceles triangle

 
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  Scalene triangle