Children

Arithmetic Progression

From Gauss's story to the justification of the formula The school narrative associated with Gauss highlights the grouping of the ends of a sum. The idea is valid beyond that story: we can demonstrate it for any finite arithmetic progression. Your turn to investigate: Write 2, 5, 8, 11, 14 and, below, the same sequence in reverse. Add the columns. Why is the result for each column the same? Discover the historical source on MacTutor, from the University of St Andrews.

April 10, 2025 Read

Nth Root

Arithmetic enzyme root Definition Given a real number $a \geq 0$ and an integer $n \geq 2$, there exists a unique real number $b \geq 0$ such that $b^n = a$. The number b we will call the arithmetic enzymatic root of a and we will indicate it by the symbol $\sqrt[n]{a}$ where a is called the radicand and n is the index. Examples $\sqrt[5]{32} = 2$ because $2^5 = 32$ $\sqrt[3]{8} = 2$ because $2^3 = 8$ $\sqrt{9} = 3$ because $3^2 = 9$ $\sqrt[7]{0} = 0$ because $0^7 = 0$ $\sqrt[6]{1} = 1$ because $1^6 = 1$ Observations

March 27, 2025 Read

Domain and Image

Domain and image Definition: Let R be a relation of A to B. The set D of all the first elements of the ordered pairs belonging to R is called the domain of R. x The set Im of all the second elements of the ordered pairs belonging to R is called the image of R. y It follows from the definition that DCA, and ImCB. Examples: If A = {0,2,3,4} and B = {1,2,3,4,5,6} what is the domain and the image of the relation R = {(x,y) E A X B y is a multiple of x}? Using the arrow scheme, it is easy to see that D is the set of elements of A from which arrows depart and that Im is the set of elements of B to which arrows arrive, meaning: R = {(2.2), (2,4), (2,6, (3,3), (3,6) (4,4),)} D = {2,3,4} Im = {2,3,4,6}

March 21, 2025 Read

Circumference ratio in regular polygons

In previous posts we talked about Stewart’s theorem, here we will talk about the circumference relationship in regular polygons. The relationship between circles and regular polygons is a fascinating and complex topic in geometry. Regular polygons are geometric figures with congruent sides and angles, and the circle can be seen as a limiting case of a regular polygon with an infinite number of sides. When a regular polygon is inscribed in a circle, each of its vertices touches the circle, and the center of the polygon coincides with the center of the circle. This allows precise relationships to be established between the radius of the circle and the dimensions of the polygon, such as the side and apothem (the distance from the center to a side).

July 18, 2024 Read

Pythagoras Theorem

The Pythagorean Theorem is one of the best-known and fundamental propositions in mathematics, establishing an elegant relationship between the sides of a right-angled triangle. The history of this theorem is as fascinating as its mathematical application, as it spans cultures and eras, revealing how mathematical knowledge is accumulated and shared across generations. Traditionally attributed to the Greek philosopher and mathematician Pythagoras, who lived between approximately 570 BC and 495 BC, the theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, known as legs.

July 11, 2024 Read

Exercises for Adding Natural Numbers

Warm-up with figures Solve first with the figures, then write the calculation on paper. Solved Exercises on Adding Natural Numbers - Elementary School Example 1: Simple sum Statement: Maria has 3 candy and John has 4 candy. How many bullets do they have together? Resolution: Maria has 3 candy and John has 4 candy. To find out how many bullets they have together, we add:

July 10, 2024 Read

Introduction to Arithmetic Progression

A school story and an idea to try A much-told story about Gauss presents him, as a boy, quickly solving a sum by grouping terms. Let’s use this narrative as an invitation to investigate patterns. Your turn to investigate: Write 1 + 2 + … + 10. Join the first term to the last, the second to the penultimate and continue. How many pairs can you get? What is the sum of each pair? Discover the historical source on MacTutor, from the University of St Andrews.

July 10, 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

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