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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

Altitude, Orthocenter of a Triangle and Triangulation

75%

Coghetto R.

Formalized Mathematics

2016

tom 24

nr 1

27-36

We introduce the altitudes of a triangle (the cevians perpendicular to the opposite sides). Using the generalized Ceva’s Theorem, we prove the existence and uniqueness of the orthocenter of a triangle [7]. Finally, we formalize in Mizar [1] some formulas [2] to calculate distance using triangulation.

Ograniczanie wyników

2 Formalized Mathematics

2 Coghetto R.

1 2016

1 2014

Wyniki wyszukiwania

Some Facts about Trigonometry and Euclidean Geometry

Altitude, Orthocenter of a Triangle and Triangulation