In any triangle that is not equilateral, the Euler line is the straight line passing through the orthocentre, circumcentre and centroid. In an equilateral triangle these three points are coincident and so do not define a line.
Euler proved the collinearity of the above three. However, there are several other important points that also lie on these lines. Amongst them,
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The centroid, orthocenter, and circumcenter of a triangle all lie on the Euler line; however, the incenter does not. The incenter, which is the intersection of the angle bisectors, represents the center of the triangle's incircle. Unlike the other three points, the incenter's position is influenced by the triangle's angles and side lengths, leading it to be generally located off the Euler line.
to draw a euler line, you must know how to draw the following terms... orthocenter, circumcenter, and centriod of a triangle, once you have drawn the following points, connect them to make a straight line, if they don't form a straight line, try again, and be as accurate as possible :)
The difference between an Euler circuit and an Euler path is in the execution of the process. The Euler path will begin and end at varied vertices while the Euler circuit uses all the edges of the graph at once.
Leonhard Euler (after whom it was named).Leonhard Euler (after whom it was named).Leonhard Euler (after whom it was named).Leonhard Euler (after whom it was named).
Euler's numberThe mathematical constant 'e' (base of the natural logarithm) was discovered by Leonhard Euler. Which explains why the number 'e' is sometimes referred to as Euler's number (not Euler's constant, which is a completely different thing).Euler did not discover e although many believe he did. Roger Cotes discovered e.