Mathematics for Children

Introduction to Quadrilaterals

In this post, the central point of the topic is quadrilaterals, which are the foundations for beginning the study of geometry. The history of quadrilaterals dates back to ancient times, with the famous Greek mathematician Euclid being one of the first to study their properties. The pioneering geometers in the study of quadrilaterals were Thales of Miletus (c. 624 – 546 BC), Pythagoras of Samos (c. 585 – 500 BC), Euclid of Alexandria (c. 365 – 300 BC).

June 6, 2024 Read

Tales' Theorem

In the previous post we talked about similarity of triangles. Now, let’s talk about Thales’ Theorem, which are fundamental concepts in plane geometry, especially in triangles. Story of Thales of Miletus Thales of Miletus was an important pre-Socratic Greek thinker, philosopher and mathematician. He is considered by some to be the “Father of Science” and “Western Philosophy”. His main ideas expanded theoretical horizons in the areas of mathematics, philosophy and astronomy. Let’s explore more about his life and contributions.

June 5, 2024 Read

Similarity of Triangles

In the previous post we talked about perpendicularity. Now, let’s talk about Similarity of Triangles, which are fundamental concepts in plane geometry, especially triangles. History of the similarity of triangles The optics used in entrance exams were discovered by Pierre Fermat in his work Variar Opera Mathematica of 1679. His original name is Clement Samuel Fermat, but he became known as Pierre Fermat. From Fermat’s studies we highlight two important results:

May 31, 2024 Read

Perpendicularity

In the previous post we talked about parallelism of triangles. Now, let’s talk about perpendicularity, which are fundamental concepts in plane geometry, especially in triangles. Perpendicularity is a fundamental concept in geometry that describes the relationship between two lines or straight segments that meet forming an angle of 90 degrees. These lines are called perpendiculars. History of perpendicularity Although there is no single specific mathematician credited with discovering perpendicularity, several ancient mathematicians and cultures contributed to the development of this concept, such as:

May 29, 2024 Read

Parallelism

In the previous post we talked about congruence of triangles. Now, let’s talk about parallelism, which are fundamental concepts in plane geometry, especially in triangles. Parallelism in geometry is a fundamental concept that describes the relationship between lines and planes. The History of Parallelism in Geometry The concept of parallelism in geometry has its roots in antiquity, specifically with the Greek mathematician Euclid, around 300 BC. He introduced the parallel postulate, which states that a single straight line passes through a point parallel to a given straight line. This postulate is one of the bases of Euclidean Geometry, which is the geometry we study on a daily basis.

May 16, 2024 Read

Congruence of Triangles

In the previous post we talked about initial concepts about triangles. Now, let’s talk about properties, specifically about the congruence of triangles. History The congruence of triangles is a fundamental concept in geometry, and its discovery dates back many centuries ago. Let’s explore a little of this story: Euclid and the Elements: The Greek mathematician Euclid, around 300 BC, formalized the principles of geometry in his famous book “The Elements”. In this work, he established the criteria for the congruence of triangles, as LLL - Side Side Side, LAL - Side Angle Side, ALA - Angle Side Angle and LAAo - Side Angle Opposite angle. These criteria are known as “congruence postulates”.

May 13, 2024 Read

Introduction to Triangles

A triangle is a three-sided polygon, in which we use straight segments for the sides. It is a particular case of quadrilaterals, as it is a quadrilateral divided by 2. Definition: Given three non-collinear points A, B and C1, the meeting of the segments $\overline{AB}$, $\overline{AC}$ and $\overline{BC}$ is called a triangle. Basic elements Vertices: can be defined as meeting points between the sides of a triangle. Generally speaking, vertices are meeting points between sides of any polygon. From the previous figure, points A, B and C are vertices of the triangle ($\Delta ABC$) In particular, a triangle is formed by 3 vertices.

May 10, 2024 Read

Right Triangles

A triangle is a three-sided polygon, in which we use straight segments for the sides. It is a particular case of quadrilaterals, as it is a quadrilateral divided by 2. Vertices: can be defined as meeting points between the sides of a triangle. Generally speaking, vertices are meeting points between sides of any polygon. In particular, a triangle is formed by 3 vertices. Diagonal: is the straight line segment that connects two non-consecutive vertices of any flat and spatial polygon. One of the important properties of triangles is that they have diagonals. An important observation is that there is no triangle that has two non-consecutive vertices. The diagonal of a quadrilateral, for example, is one of the sides of a triangle.

May 4, 2024 Read

Natural Number Subtraction Exercises

Warm-up with figures Make a similar drawing for the first subtraction from the list. Solved Subtraction Exercises - Elementary School I Simple Subtraction Statement: João had 10 bullets and gave 4 to his friend. How many bullets does João have now? Resolution: To find the amount of candy that John now has, we subtract the amount he gave from the initial amount he had:

January 10, 2024 Read

OBMEP 2022 - Second Phase - Level 1

OBMEP 2021: Second Phase - Level 1 Exercise 1 On the board, each letter of the word OBMEP represents an integer from 1 to 5. Different letters represent different numbers. Furthermore, each number written on the side of the board is the sum of the values of the letters on the board. corresponding horizontal line. A) Find the value of the letter O. Response: 1 When we add the values from the first line, we have

July 1, 2023 Read

First Degree Functions

The beginning of learning about functions goes through first degree functions. In this post, we will present some first-degree functions. Among them are constant, linear and related. Constant function The constant function is a plateau, something flat or simply a horizontal line. Below we present the formal definition. Definition (Constant Function): an application $f$ of $\mathbb{R}$ in $\mathbb{R}$ is called a constant function when each element $x \in\mathbb{R}$ always associates the same element $c \in\mathbb{R}$.

November 28, 2022 Read

Dispersion Measures

Dispersion measures are fundamental, because unlike mathematics, statistics work with random variables. For example, the big media worked with deterministic values, such as candidate A has 45% and B with 30%. For mathematics, A is clearly ahead, but for statistics, I don’t know. Today they present it in a statistical way, as they talk about the “margin of error”. If the “margin of error” is 15%, the two are technically tied.

November 27, 2022 Read