Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: circumcircle

Sortuj według:

Ogranicz wyniki do:

Some Facts about Trigonometry and Euclidean Geometry

100%

Coghetto R.

Formalized Mathematics

2014

tom 22

nr 4

313-319

We calculate the values of the trigonometric functions for angles: [XXX] , by [16]. After defining some trigonometric identities, we demonstrate conventional trigonometric formulas in the triangle, and the geometric property, by [14], of the triangle inscribed in a semicircle, by the proposition 3.31 in [15]. Then we define the diameter of the circumscribed circle of a triangle using the definition of the area of a triangle and prove some identities of a triangle [9]. We conclude by indicating that the diameter of a circle is twice the length of the radius

Circumcenter, Circumcircle and Centroid of a Triangle

75%

Coghetto R.

Formalized Mathematics

2016

tom 24

nr 1

17-26

We introduce, using the Mizar system [1], some basic concepts of Euclidean geometry: the half length and the midpoint of a segment, the perpendicular bisector of a segment, the medians (the cevians that join the vertices of a triangle to the midpoints of the opposite sides) of a triangle. We prove the existence and uniqueness of the circumcenter of a triangle (the intersection of the three perpendicular bisectors of the sides of the triangle). The extended law of sines and the formula of the radius of the Morley’s trisector triangle are formalized [3]. Using the generalized Ceva’s Theorem, we prove the existence and uniqueness of the centroid (the common point of the medians [4]) of a triangle.

Ograniczanie wyników

2 Formalized Mathematics

2 Coghetto R.

1 2016

1 2014

Wyniki wyszukiwania

Some Facts about Trigonometry and Euclidean Geometry

Circumcenter, Circumcircle and Centroid of a Triangle