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Inscribed angle

In previous posts we talked about properties of circular arcs. Now, we talk about angles inscribed in a circle. An inscribed angle is one whose vertex is on a circle and whose sides are secants that intersect the circle at two other distinct points. The most notable property of an inscribed angle is that its measure is equal to half the measure of the arc it subtends on the circumference.

July 4, 2024 Read

Arches Properties

In previous posts we talked about circumscribable segments. Now, we talk about properties of circular arcs. An arc of a circle is a portion of a circle bounded by two points. The circumference, in turn, is the set of all points equidistant from a central point in a plane. One of the properties is the congruence of arcs. Two arcs are congruent (that is, they have the same measure) if they subtend congruent central angles. This is useful, for example, in constructing regular polygons inscribed in a circle, where all sides and angles are equal.

July 3, 2024 Read

Circumscript segments

In previous posts we talked about positions relative to the circumference. Now, we talk about circumscriptive segments. Geometry is a fascinating area of mathematics that studies the properties and relationships of points, lines, angles, surfaces and solids. Within this vast field lie circumscriptive segments, which play a crucial role in many aspects of geometry and beyond. Circumscript segments refer to line segments that connect points on the circumference of a circle or other geometric figure. These segments are fundamental for understanding inscribed and circumscribed figures, which are figures drawn inside or outside another figure, respectively.

July 2, 2024 Read

Position relative to the Circumference

In previous posts we talked about Introduction to Circumference. Mathematics is a fascinating science that allows us to understand and describe the world around us with precision and beauty. One of the most interesting topics within geometry is the study of the relative positions between straight lines and circles. This field of study has a rich history, marked by significant discoveries made by mathematicians over the centuries. The relative positions of a straight line in relation to a circle can be classified into three main categories:

July 1, 2024 Read

Introduction to Circumference

In previous posts we talked about Polygons. Now, let’s talk about Circumference. The circle, one of the most perfect and fundamental shapes in geometry, has fascinated mathematicians throughout history. The quest to understand its nature and properties has led to significant discoveries that have shaped not only the field of mathematics but also the way we view the world. History The relationship between the diameter and length of a circle, known as π (pi), is a constant that has intrigued mathematicians for centuries. The search for this constant has led to significant advances in mathematics and understanding of the physical universe.

June 28, 2024 Read

Polygon Properties

In previous posts we talked about regular polygons. Now, let’s talk about the properties of polygons. Constituent Elements Each polygon is made up of fundamental elements such as vertices, sides, diagonals and internal and external angles. Vertices are the points where two sides meet, and sides are the line segments that connect these vertices. Diagonals are straight segments that connect two non-consecutive vertices, and internal angles are formed by the intersection of two consecutive sides.

June 28, 2024 Read

Regular Polygons

In previous posts we talked about some concepts about polygons in general. Regular polygons are closed, flat and fascinating geometric figures that have aroused the interest of mathematicians and artists throughout history. Characterized by having all sides and internal angles congruent, these figures are the embodiment of symmetry and harmony. A flat geometric figure with sides of equal length and internal angles of equal measure. This means that a regular polygon not only looks balanced, but also follows precise mathematical rules that can be expressed through elegant and useful formulas.

June 27, 2024 Read

Introduction to Polygons

In previous posts we talked about triangles. Now, let’s talk about Polygons. Polygons are fascinating geometric figures that have been an integral part of mathematics and human culture since time immemorial. The word “polygon” originates from the Greek “polígonos”, which means “many angles” and reflects the nature of these shapes, limited by straight lines and a variable number of sides. History Polygons have a fascinating history, from their discovery by ancient mathematicians to their application in various areas of knowledge. The first records of polygons date back to antiquity, in the Egyptian and Mesopotamian civilizations. Ancient people already used these shapes to measure land, build monuments and even to symbolize religious concepts.

June 25, 2024 Read

Notable points of the triangle

In the previous post we talked about Thales’ theorem. Now, let’s talk notable points of the triangle. History The term “ceviana” comes from the name of the Italian mathematician Giovanni Ceva. A cevian is a line segment that connects a vertex of a triangle to any point on the line that contains the opposite side. The notable points of the triangle came from studies of Cevians. Examples of cevians include the median, height, and bisector. The median, for example, connects the vertex from which it starts to the midpoint of the side opposite that vertex. The barycenter is the meeting point of the medians and represents the center of gravity of the triangle.

June 25, 2024 Read

Rectangle, Rhombus and Square

In this post the central point of the theme is the Rectangle, Rhombus and Square, as well as their properties. The history of squares and rectangles dates back to antiquity, when civilizations such as the Egyptian and Mesopotamian already used these geometric shapes to measure land, build monuments and symbolize religious concepts. Introduction Notable quadrilaterals are geometric figures that play a fundamental role in mathematics. Let’s explore its historical origin and properties.

June 18, 2024 Read

Parallelogram

In this post the central point of the topic is Parallelograms, as well as their properties. A parallelogram is a quadrilateral with four sides, where opposite sides are parallel. Introduction Every parallelogram has rectangle, rhombus and square as subsets. Definition: A convex flat quadrilateral is a parallelogram if, and only if, its opposite sides are parallel. $\overline{AB}$, $\overline{BC}$, $\overline{CD}$ and $\overline{DA}$ are parallel. General concepts of the Parallelogram Opposite sides of a parallelogram are congruent, that is, they have the same measurement. Opposite angles of the parallelogram are congruent (same measurement). The consecutive angles of the parallelogram are supplementary, whose sum totals 180°. The sum of internal or external angles adds up to 360°. The diagonals of the parallelogram intersect at their respective midpoints (middle of the figure). A little of history The history of the parallelogram in mathematics is intrinsically linked to the evolution of geometry. The parallelogram, like a quadrilateral with opposite sides parallel, is a fundamental figure in plane geometry.

June 14, 2024 Read

Trapeze

In this post the central point of the topic is trapezoids, as well as their properties. A trapezoid is a flat geometric figure formed by four sides. Two of them are parallel and are called bases. The geometry of the trapezoid has its roots in Ancient Greece, where mathematicians such as Euclid and Archimedes studied its properties1. The name “trapezium” comes from the Greek trapezion, which means “square table”. The trapeze was also used by the Egyptians in the construction of pyramids and temples.

June 7, 2024 Read