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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.
- Orthocentre = point of intersection of altitudes.
- Circumcentre = point of intersection of perpendicular bisector of the sides.
- Centroid = point of intersection of medians.
Euler proved the collinearity of the above three. However, there are several other important points that also lie on these lines. Amongst them,
- Nine-point Centre = centre of the circle that passes through the bottoms of the altitudes, midpoints of the sides and the points half-way between the orthocentre and the vertices.
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How do you draw Euler's 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 :)
What is the difference between an Euler circuit and an Euler path?
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.
Who calculated the value of e?
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).
Who discovered e in maths?
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.
What is the number e?
It is Euler's number which is the base of natural logarithms.
