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Subtraction. Properties
39 - 28 = 11 (It reads: The difference between thirty-nine and twenty-eight is equal to eleven.)
39 (Additive), 28(Subtractive) and 11(Difference)
Note: To check whether the subtraction is carried out correctly, the fundamental property of subtraction can be applied:
The sum of the subtractive and the difference is equal to the additive.
To make an estimate of a difference, we normally round the numbers to the nearest tens or hundreds.
903 + 288 = 615 (Exact value)
900 - 300 = 600 (Estimate)

A quadratic equation, or quadratic equation, is a polynomial equation with the highest degree equal to 2. It is represented in the general form: ax^2 + bx + c = 0, where a, b and c are constants and x is the variable unknown. There are three possible types of solutions for a quadratic equation: Two real and distinct roots: When the discriminant (∆) of the equation is greater than zero (∆ > 0), the equation has two different real roots. Two real and equal roots: When the discriminant is equal to zero (∆ = 0), the equation has two real roots that are equal, resulting in a unique solution.No real roots: When the discriminant is less than zero (∆ < 0 ), the equation has no real roots. In this case, the roots can be complex conjugate numbers.

A first-degree equation is a polynomial equation whose highest degree is 1. It is expressed in the general form: ax + b = 0, where a and b are known constants, and x is the unknown variable. The solution of a first-degree equation is a specific value of x that makes the equality true. To solve the equation: Isolation of the term with the unknown: Transfer the term containing the variable to one side of the equation, so that it remains alone. All other terms carry over to the other side. Simplification of the equation: Perform the necessary mathematical operations to simplify the equation. Variable isolation: Divide both sides of the equation by the coefficient of x to isolate the variable. Solution of the equation: The value of x that makes the equality true is obtained, called the solution of the equation. A first-degree equation has a unique solution, unless it is an identity equation, where any value of x satisfies the equality.

A set is a collection of distinct elements grouped into a single entity. Elements can be numbers, objects, people or anything that can be uniquely identified. Sets are represented between braces {}. Some important concepts related to sets include: Membership: An element can belong to a set. If an element is present in a set, it is said to belong to that set. Empty set: It is a set that has no elements. Subset: A set is considered a subset of another set if all its elements also belong to the larger set. Union: The union of two sets is a new set that contains all the elements of the original sets, without repetitions. Intersection: The intersection of two sets is a new set that contains only the elements common to both sets.

November 23rd Fibonacci Day. The date was chosen because, when referring to the Fibonacci sequence, which is a numerical series in which each number is the sum of the two previous ones (0, 1, 1, 2, 3, 5, 8, 13, 21, etc.), the sequence can be represented by the pair of numbers (1, 1) on November 23rd, if we consider the numbers 23 and 11. The origin of the celebration goes back to the Italian mathematician Leonardo de Pisa, known as Fibonacci, who lived in the 13th century. He is famous for having introduced the Fibonacci sequence to the Western world through his book Liber Abaci, published in 1202. The sequence not only appears in various areas of mathematics, but also manifests itself in natural patterns, such as the arrangement of leaves on a plant, the reproduction of rabbits and the structures of flowers.

The Rubik's Cube, created by Hungarian architect and architecture professor Ernő Rubik in 1974, has become one of the world's most popular puzzles and a true cultural icon. Originally invented by Rubik as a teaching tool to teach his students about geometry and spatial transformations, it quickly became a worldwide challenge.
The 3x3x3 cube, the best-known version, has around 43 quintillion possible combinations (43,252,003,274,489,856,000), but only one unique solution. This staggering number of possibilities reflects the complexity of the cube and why it has fascinated so many people over the years. Despite its difficulty, the Rubik's Cube has also spawned a global phenomenon of "speedcubing", where competitors aim to solve the cube as quickly as possible. The current record for solving the 3x3x3 cube is 3.13 seconds, an impressive feat that demonstrates the skill and practice involved in this art.
In addition to the classic model, the Rubik's Cube has inspired a number of variations. There are cubes with larger sizes, such as the 4x4x4, 5x5x5 and even more complex versions, such as the 11x11x11 cube. These variations significantly increase the complexity and number of combinations, providing even greater challenges for enthusiasts.

The equality symbol (=), used universally in mathematics and in various areas of knowledge, has an origin that dates back more than 450 years. Created by the English mathematician Robert Recorde in 1557, the symbol arose from a simple but powerful idea: "no two things can be more equal than two parallel lines". This phrase was Recorde's inspiration to create the symbol that, to this day, we use to indicate that two expressions have the same value.
Before the invention of the equality symbol, equations were expressed in a more verbal way, which made calculations more complicated. Recorde, in looking for a way to simplify mathematical notation, created a symbol that could clearly and quickly represent this relationship of equality. The choice of two parallel lines reflects the idea of ​​balance and symmetry, concepts that are fundamental in mathematical operations.
The equality symbol was introduced in his work The Whetstone of Witte and, over time, was widely adopted by the mathematical community. Today, it is one of the most recognized symbols in the world, not only in mathematics, but also in areas such as logic, programming and science in general, being essential in the construction and solution of equations and formulas.

The year 2025 brought a unique and fascinating mathematical coincidence. In addition to being a perfect square, since 45² (45 x 45) results in 2025, it also presents a curious sum of cubes. 2025 is equal to the sum of the cubes of the first nine consecutive integers: 1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + 8³ + 9³, which is also exactly 2025.
This mathematical relationship is rare and has not occurred since the year 1296, and will not be repeated until the year 3025. The idea that 2025 can be expressed both as the square of 45 and as the sum of the cubes of consecutive numbers adds a layer of complexity and beauty to mathematics, showing how certain numbers have properties that make them special and unique.
Coincidences like this, which involve both simple operations and more complex concepts, are always a delight for mathematicians. They remind us that numbers, even in their simplest form, are full of surprises and unexpected relationships. The year 2025, therefore, will be marked by this intriguing mathematical peculiarity, which makes us look at numbers in a new and fascinating way.

The infinity symbol (∞) is widely recognized in areas such as mathematics, philosophy and other sciences, and is associated with the idea of ​​something that has no end. Its origin dates back to the 17th century, when the English mathematician John Wallis introduced it in his work Arithmetica Infinitorum, in 1656, to represent an infinite quantity. However, Wallis never clearly explained why he chose this symbol, which has given rise to some theories about its origin.
One of the most widely accepted explanations is that Wallis was inspired by the Roman symbol for the number one thousand, "CIƆ", used in ancient Rome to represent large quantities. Another interesting fact is that the infinity symbol is also known as lemniscate, which comes from the Latin lemniscatus, meaning "decorated with ribbons". This term is related to a geometric curve, the "eight", which mathematicians such as Jakob Bernoulli studied, representing the concept of something without end.
In addition to being used in mathematics, the symbol also appears in philosophy, to express ideas of eternity and infinite time, and in astronomy, in curves such as the "ring", which represents the path of the sun throughout the year.
Over time, the symbol became popular and became an essential element in mathematical notation, helping to express concepts such as continuity and limits.

Malba Tahan's famous book, "The Man Who Counted", describes a theory known as "four fours". This technique allows the formation of any integer between 0 and 100 using only four numerals 4 and mathematical operation signs. For example, to get a “3”, just perform the operation (4+4+4)/4.

The golden number is a fascinating mathematical theory and one that is surrounded by myths. Represented by the Greek symbol Phi (f), this number, 1.6180, is the diagonal/side ratio of a regular pentagon and has been studied since antiquity. It indicates harmony, which is why it is present in works by Leonardo da Vinci, in constructions such as the Pyramids of Egypt and even in the size of human phalanges.

While many young people today are looking for fun in video games or sports activities, Evariste Galois opted for a different path: furthering his studies in Mathematics. Considered one of the most brilliant thinkers in the scientific field, Galois even challenged teachers and preferred books by renowned geniuses over classes. Although he left only 60 pages of notes, his legacy was considered fundamental for the development of Mathematics. Tragically, his life came to an untimely end, for in 1832 Galois defended honor in a tragic way: he took a pistol and died in a duel.

The professor had his students add up all the numbers from one to one hundred, and was amazed to see that young Gauss got the correct answer, 5,050, in a few seconds. What made the boy realize this account so quickly was his ability to observe and calculate that if he added the first number to the last, 1 + 100, he got 101. When he added the second number to the next to last, 2 + 99, The result was also 101. So Gauss discovered that adding all the numbers from one to one hundred was the same as adding 50 times the number 101, which is 5,050. This was the first time that he invented the formula for the sum of arithmetic progressions, as a child. Gauss, who lived between 1777 and 1855, is considered by many to be the greatest mathematical genius of all time, and is therefore known as the Prince of Mathematics.

Approximately 8 x 10^67 different ways can be used to sort a deck of cards. To put this in perspective, even if someone turns over a deck of cards every second since the beginning of the universe, it would still be impossible to find a repeat before the universe comes to an end.

It is not possible to comb all the hairs on a tennis ball in the same direction. This mathematical problem is known as Henri Poincaré's theorem. It was formulated at the end of the 19th century and can be mathematically described as "there is no non-disappearing continuous tangent vector field in even-dimensional n-spheres". However, it is most easily expressed as "you can't comb a furry ball without creating a quiff". This theorem was confirmed by Brouwer in 1912, and it has an interesting consequence: on an ideal spherical planet, there is at least one point where the wind is blowing. The planet doesn't have to be perfectly spherical, but it should be continuous - meaning it shouldn't have holes or bumps in the middle.

The number pi is found everywhere. His involvement with circles is well known, but it also crops up in other settings. For example, the series 1/1 2 + 1/2 2 + 1/3 2 + 1/4 2 + 1/5 2 … = 1 + 1/4 + 1/9 + 1/16 + 1/25 .. . gets closer and closer to the value π2 / 6 = 1.645... as more and more terms are added. Flipping this fraction around, we get 6/π2, which is equal to the probability that two numbers, provided they are large enough, are prime—that is, that they have no common factors other than 1.

Mathematics offers us a curious discovery, known as the Horn of Gabriel. This surface is formed by rotating the curve y = 1/x, a rectangular hyperbola, around the x axis for values greater than one. The remarkable fact discovered by Italian physicist and mathematician Evangelista Torricelli is that although the Horn has a finite volume, equal to π cubic units, its surface area is infinite. If the Horn were filled with ink, there would not be enough ink to cover its entire area.

The Fibonacci Sequence is famous for being found in nature. The process to create the sequence is to add two previous integers to generate the next one. For example, starting with 0 and 1, the sequence goes like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etc. This sequence was discovered during an experiment on the growth of rabbits. Also, the song "Lateralus" by the American prog metal band Tool is composed following the Fibonacci sequence.

Roman numerals were originally developed for trading purposes. They were widely used throughout the Roman Empire for accounting purposes, allowing Romans to quickly transact products and services. After the fall of the Roman Empire, this form of numbering was adopted throughout Europe. However, it was gradually replaced by other numbering systems from the 16th century onwards.

We know what a light year is: a unit of length that indicates the distance traveled by light in one year. Light develops a speed of 300,000km/s, which means that, in one second, it travels 300,000km. So, in one year, it travels 9,460,800,000,000Km, more than 9 trillion kilometers! When someone says that a galaxy is 10 light years away from Earth, it means that it is at a distance of 90 trillion kilometers

It was noted that four-legged chairs usually present imbalance, while three-legged ones do not. Mathematics explains this fact, but it is difficult to understand. To understand why, look at a farm gate. It has a diagonal board, forming two triangles. In this way, it is more resistant to deformation and the maintenance of its balance is guaranteed. Likewise, the three legs of a chair form a triangle, making it more robust and stable.

Why do we write numbers the way we know them? If you thought someone just decided it was going to be that way, you're wrong! Behind this writing there is an explanation. Each of the numbers between 0 and 9 was created based on the number of angles it has. For example, the number 3 is represented by a symbol with 3 angles. Check the representation on the side.

Since antiquity, numbers have been used to count objects and animals. The Egyptian people were one of the first to create a numbering system, in the year 3000 BC. Other peoples were also creating their own counting methods, such as the Romans, who created Roman numbers, which are still used today for clocks, books and in counting centuries. However, the numbering system we use today was created by the Indians in North India in the 5th century.

Number 1089 is known as magic number. To get it, choose a number with three different digits, such as 683. Write the number you chose and subtract it backwards: 723 -327 = 396. Finally, take the result and add it backwards forward: 396 + 693 = 1089, which makes 1089. This calculation works with any three-digit number.

There is a mathematical calculation of 4 steps that will always result in the number 6. Come on, the first step is: (1) Think of a number, for example: 104; (2) Multiply it by 2: 104 x 2 = 208; (3) Now add 12 to the value: 208 + 12 = 220; (4) The next step is to divide the result by 2: 220 / 2 = 110; (5) And finally, take the value obtained in the calculation and subtract the initial number: 110 – 104 = 6. The explanation behind this result always giving 6 is in algebra.

International Mathematics Day is celebrated on March 14 , known as Pi Day due to the numerical representation of the date (3/14), which corresponds to the first digits of the number pi. As of 2020, by decision of UNESCO, the day began to be officially recognized to celebrate the importance of mathematics around the world. Each year has a specific theme, and celebrations include a variety of educational events and activities to promote interest and understanding of mathematics.