Retta

Concept — Retta.

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Linked atoms

60 linked atoms.

08 Fondamenti di geometria euclidea

• Angles formed by parallel lines and a transversal
• Bisector, median and altitude
• Distance of a point from a line
• Proofs using parallelism
• Sum of the interior angles of a triangle
• The intercept theorem
• The parallelogram
• The rhombus and the bisecting diagonal

12 La parabola

• Line tangent to the parabola
• Mixed cases with two absolute values

16 Circonferenza

• Angle bisector theorem
• Distance of a point from a line
• Incentre - concurrency of the bisectors
• Point on a parabola at a given distance

17 Disequazioni irrazionali

• Application — lines at an assigned distance
• Distances in analytic geometry
• Example — distance in a pencil of lines

18 Fasci di rette

• Complete study of a pencil
• Example — Fixed distance
• Example — Secant, tangent, external
• Proper and improper pencils compared
• The improper pencil
• The proper pencil
• The strategy for determining the parameter

19 Luoghi geometrici nel piano cartesiano

• Bisectors of two given lines
• Bisectors of two lines
• Locus
• Parabola from focus and directrix
• Parabola from focus and directrix
• Perpendicular bisector of a given segment
• Perpendicular bisector of a segment
• The bisector as a locus
• The parabola as a locus
• Why the locus is a line

20 Circonferenza nel piano cartesiano

• Circle tangent to two lines: the angle-bisector trick
• Example — tangents with the delta method
• Example — tangents with the distance method
• Relative positions of a line and a circle
• Tangent at a point of the circle
• Tangents with the distance method
• The delta method and the distance method
• The method of tangents from a point

28 Circonferenza goniometrica e funzioni sin, cos, tan

• arctan and the gradient
• Worked examples of the inverses

37 Geometria analitica nello spazio

• Cartesian form of the line
• Distance between two skew lines
• Example - skew lines
• Line-plane and plane-plane distances
• Parametric form of the line
• Parametric-Cartesian conversion
• Point-line distance
• Point-line distance
• Relative position of two lines
• Relative positions of line and plane and angles
• The four cases

41 Continuità e discontinuità

• Newton exact for linear functions
• The Newton-Raphson method

42 Derivate

• Tangent and normal to eˣ
• Tangent line and normal line
• The derivative as the slope of the tangent