For the third-year undergrads!
Watch the video and answer the questions:
1) Where is geometry used nowadays? 2) In what way did geometry pass to the next generations? 3) What is Thales and what is his contribution to the development of geometry? 4) What new information about Euclid did you obtain? 5) How is Euclid called and why? 6) What terms are considered underfined and why? 7) What is an axiom/ a postulate/ a theorem? 8) What are they for? 9) What is Euclid's fifth axiom about? 10) What is the role of geometry?
1. Nowadays geometry is found everywhere, for example in nature, in space, in art and in architecture.
ОтветитьУдалить2. At this time old developments were passed down to the next generation without being discussed and proved.
3. Thales is a first mathematician who give fast know proving in geometry.
4. That Euclid was a mathematics teacher in Egypt.
5. The father of geometry, because he made a great contribution to its development.
6. Terms which were left undefined and the reason for doing so.
7. An axiom is a statement accepted as true without proof, and which subsequently serves as a "foundation" for constructing proofs within the framework of a theory, discipline, etc.
A postulate is a statement that is accepted without evidence, and serves as the basis for the construction of any scientific theory.
A theorem is a statement for which there is a proof (in other words, a conclusion) in the theory under consideration.
8. They serve to solve any emerging problems.
9. If the sum of the internal angles with a common side formed by two straight lines at the intersection of their third, on one side of the secant is less than 180 °, then these lines intersect, and moreover on the same side of the secant.
10. Geometry improves many foundations skills:
1. Logical reasoning.
2. Analytical reasoning.
3. Problem solving skills and etc.
1) Geometry is used in many fields today, including architecture, engineering, physics, computer graphics, and more.
ОтветитьУдалить2) Geometry has been passed on to the next generations through written works and teaching.
3) Thales was a Greek mathematician who lived around 600 BCE and is considered one of the Seven Sages of Greece. His contribution to the development of geometry includes his theorem about the angles of a triangle, which states that the sum of the angles of a triangle is equal to two right angles.
4) The question mentions a video, but does not provide any specific information about the video, so I cannot answer this question.
5) Euclid is called the "father of geometry" because he wrote a comprehensive treatise on geometry, called "Elements," which was used as a textbook for over 2,000 years.
6) In geometry, some terms are considered undefined, such as point, line, and plane, because they are basic concepts that cannot be defined in terms of simpler concepts.
7) In geometry, an axiom is a statement that is accepted as true without proof and is used as a basis for further reasoning and deduction. A postulate is a statement that is accepted as true without proof and is used as a basis for further reasoning and deduction. A theorem is a statement that can be proved from axioms and other theorems.
8) Axioms, postulates, and theorems are used in geometry to establish a logical framework for reasoning and deduction.
9) Euclid's fifth axiom, also known as the parallel postulate, states that if a line intersects two other lines and the interior angles on one side of the intersection add up to less than two right angles, then the two lines will eventually intersect on that side. This axiom was controversial and led to the development of non-Euclidean geometries.
10) The role of geometry is to provide a framework for understanding and describing the physical world around us, and for developing new technologies and solving real-world problems.
Магомедов Мурад
http://maths-dgu.blogspot.com/2023/04/blog-post.html?m=1
1)The geometry used in nature, space, art and architecture;
ОтветитьУдалить2)All the developments were passed on to the next generation without being discussed or proved;
3)Thales was the first mathematician who gave first known prove in geometry;
4)I obtained that in “Elements” was 13 chapters;
5)The Father of geometry. Because "Elements" contains almost everything which you can know about plane geometry and 3d figures;
6)In geometry, point, line, and plane are considered undefined terms because they are only explained using examples and descriptions;
7)Axioms or postulates are universal truths.They cannot be proved.Usually, postulates are used for universal truths in geometry, and axioms are used everywhere. Though, both mean the same thing.Theorem are statements which can be proved;
8)Axioms and postulates are used as the basis of proof.Theorems are needed to simplify the solution of problems in geometry;
9)If a line falling on two lines forms one-sided interior angles less than two lines in sum, then, extended indefinitely, these two lines will meet on the side where the sum of the angles is less than two lines;
10)Geometry gives not only an idea of the figures, their properties, relative position, but also teaches you to reason, ask questions, analyze, draw conclusions, think logically.
1. Currently, geometry is used in nature, space, art and architecture.
ОтветитьУдалить2. Geometry passed on to the next generations without discussion and confirmation.
3. Thales is an ancient Greek philosopher and mathematician who was the first to formulate and prove several geometric theorems.
4. New information according to the video is that Euclid was a math teacher in Egypt.
5. Euclid is known as the "father of geometry" because his book "Elements" is divided into 13 chapters, which contains everything about planimetry and solid geometry.
6. In geometry, there are terms that are considered indefinite: point, straight line and plane. These concepts are basic and are explained only using descriptions and examples.
7. An axiom is an unquestionable statement; a postulate is a statement accepted without proof, but which can be refuted by experience; a theorem is a mathematical statement whose truth is established by proof.
8. They simplify the introduction of concepts and help to solve various tasks.
9. Euclid's 5th axiom states: "If a straight line passing through two straight lines forms internal and on one side angles smaller than two straight lines, then these continuing straight lines will intersect infinitely on the side where the angles are less than two straight lines."
10. Geometry introduces us to the surrounding reality, gives us the spatial representations necessary for every person, introduces us to a variety of spatial forms, the laws of their perception.
Абдусамадов Магомедтагир (3к, 2гр)
ОтветитьУдалить1. geometry currently used in nature, space, art and architecture
2. geometry passed on to the next generations without discussion or proof
3. he is the first mathematician to prove that a circle is bisected by its diameter.
4. for me the new information was that he was a mathematics teacher in Egypt.
5. Euclid has been called the "father of geometry" known for the knowledge he brought and the books he wrote, one such book is "The Elements"
6. the terms point, line, and plane are considered undefined because they are basic concepts that cannot be defined in terms of simpler concepts.
7. An axiom is an initial position about the properties of geometric figures, which is accepted without proof.A postulate is a statement that is accepted as true without proof and is used as a basis for further reasoning and conclusions. A theorem is a statement whose truth is established by proof.
8. hey make it easier for us to solve problems
9. Euclid's fifth axiom says that if a line falling on two lines forms one-sided interior angles less than two lines in sum, then, continuing indefinitely, these two lines will meet on the side where the sum of the angles is less than two lines.
10. Geometry improves many foundation skills: logical reasoning, analytical reasoning, problem solving skills ect
1) Geometry is utilized in various fields such as nature, space, art, and architecture
ОтветитьУдалить2) Geometry was passed down to subsequent generations without extensive discussions or proofs
3) Thales is recognized as the first mathematician who provided a known proof in geometry, specifically demonstrating that a diameter bisects a circle into halves
4) New information suggests that Euclid was a mathematics teacher in Egypt
5) Euclid is commonly referred to as "the father of geometry" because he wrote a book called "Elements," which covers a wide range of statements and proofs in both plane and three-dimensional geometry
6) In geometry, the terms considered undefined are a point, a line, and a plane. They are left undefined because they serve as the foundational concepts from which other geometric concepts are built
7) An axiom and a postulate are statements in geometry that are accepted as true without requiring proof. A theorem, on the other hand, is a statement that has been proven to be true through a logical proof
8) Axioms, postulates, and theorems serve the purpose of establishing a logical framework and foundation for solving mathematical problems in geometry
9) Euclid's fifth axiom, also known as the parallel postulate, states that if a line segment crosses two other lines in such a way that the sum of the interior angles on one side is less than 180 degrees, then those two lines will eventually meet on that side
10) Geometry plays a crucial role in developing logical thinking skills, deductive reasoning, analytical reasoning, and problem-solving abilities. It provides a framework for understanding spatial relationships and is applicable in various fields such as engineering, architecture, physics, and computer graphics
Imanalieva Z.
ОтветитьУдалить1. Geometry plays an important role in nature, space, art, and architecture today.
2. Geometry has been passed down to the next generation without any debates or proofs.
3. Thales was the first mathematician to prove that a circle is bisected by its diameter.
4. From the video, I learned that Euclid was a mathematics teacher in Egypt.
5. Euclid's book, "Elements," is divided into 13 chapters and contains almost everything one needs to know about plane geometry, spheres, and other figures, which is why he is known as "the father of geometry."
6. The fundamental concepts in geometry are points, lines, and planes.
7. Postulates and axioms are statements that are accepted as true without proof, while theorems must be proven.
8. Axioms and postulates make it easier for us to solve mathematical problems, such as using them to prove theorems or solve specific problems.
9. Euclid's fifth axiom states that if a straight line falls on two other straight lines and the interior angles on the same side are less than two right angles, then the two straight lines will meet on that side where the sum of angles is less than two right angles.
10. Geometry plays a crucial role in helping people develop their logical thinking skills, deductive reasoning, analytical reasoning, and problem-solving abilities.
1. Geometry is used nowadays everywhere : nature, art, architecture and space
ОтветитьУдалить2. Many years ago geometry passed to the next generations without being discussed or proved
3. Thales is Greek mathematician who discovered that a diameter bisects any circle
4. Euclid wrote a book called “Elements”. It consists of 13 charters each called “Book” and includes knowledge of plane and 3-dimensional figures
5. Euclid is called “The father of geometry” because of his contribution in the development of geometry
6. A point, a line and a plane. They are considered as axioms in geometry
7. An axiom and a postulate are the statements are accepted to be true without any proof, but according to Euclid a postulate is more specific than an axiom. A theorem is a statement too, but it must be proven
8. All axioms, postulates and theorems are used for easier solving different kinds of problems in math
9. About parallel : “Through a point not on line L, there is only one parallel to L”
10. Geometry helps us in improving different kinds of skills like logical thinking, deductive reasoning, analytical reasoning, and problem-solving
Шуайбов Шуайб
1. it’s used in nature, space, architecture and art
ОтветитьУдалить2. without proofs or discussions
3. Thales is a ancient Greek philosopher and mathematician. His contribution to the development of geometry is that he was the first who proved that the circle is bisected by a diameter
4. i didn’t know that he was teacher of maths in Egypt
5. Euclid is called “the father of geometry”. he wrote a book called “Elements” about 2D and 3D figures and not just that. this book made a big contribution in the development of geometry and gave the beginning of the Euclidean geometry
6. there are three terms that are considered underfined : a line, a place and a point
7. a theorem is a statement that is accepted to be true always with a proof. an axiom and a postulate mean the same, they both mustn’t be proven
8. axioms, postulates and theorems help us solve problems of all branches of geometry
9. the fifth Euclidean postulate is about parallel : «if a line falling on two lines forms interior angles on one side of it, taken together, is less than two right angles, then two lines, if drawn indefinitely, will meet on the side on which the sum of the angles is less than two right angles»
10. geometry improves our logical thinking skills, problem-solving, deductive reasoning and analytical reasoning skills.
1) Geometry is used in many fields, including architecture, engineering, design, physics, computer graphics, and even in medicine and biology.
ОтветитьУдалить2) Geometry was passed on to the next generations through books, textbooks, lectures and modern technologies
3) Thales of Miletus was an ancient Greek philosopher and mathematician who made an important contribution to the development of geometry
4) Euclid taught mactematics in a library in Egypt
5) Euclid is also called the "father of geometry".
6) Undefined terms are concepts such as point, line and plane, because they cannot be defined more specifically within geometry without using other undefined terms.
7) An axiom is a statement that is accepted without proof and is considered true; a postulate is the main statement that is necessary to prove a theorem; a theorem is a statement that can be proved on the basis of axioms and postulates.
8) Axioms, postulates and theorems are necessary to establish logical patterns in geometry, the initial description of the properties of mathematical objects and the solution of various problems.
9) Euclid's fifth axiom, also known as the axiom of Parallelism, establishes the properties of parallel lines and is one of the basic principles of geometry.
10) Geometry plays an important role in mathematics, science and technology, helping us to understand the properties of space and shape, as well as use this knowledge to create new technologies and algorithms.
Талибова Амина
ОтветитьУдалить1) Used in various fields: engineering, computer graphics, mathematical sciences, physics and others.
2) Passed down from generation to generation through textbooks and scientific papers.
3) Thales is a Greek philosopher and mathematician who made development in geometry, he formulated the theorem on right angles in a triangle, studied circles and their properties.
4) New information about Euclid includes various aspects of his work: his contribution to the development of geometry, his work "Elements", his methods and approaches to the study of mathematics.
5) Euclid, an ancient Greek mathematician who lived in the III - II centuries BC, the author of "Beginnings", one of the most important works on geometry.
6) Underdetermined terms in geometry "point", "line" and "plane".
7) An axiom is a statement that is accepted as true within the framework of a given theory without requiring proof and is used in proving its other provisions, which, in turn, are called theorems.
8) for the development and justification of geometric concepts and theories.
9) Euclid's fifth axiom of parallel lines says that through a point that does not lie on a given line, only one line can be drawn parallel to the given line.
10) Geometry gives not only an idea of figures, their properties, relative position, but also teaches you to reason, ask questions, analyze, draw conclusions, think logically.
1)geometry is used in many fields: architecture, construction, engineering, graphics and design, cryptography, medicine, physics and mathematics
ОтветитьУдалить2)Geometry was passed on to the next generations through training courses in schools and universities
3)Thales is an ancient Greek mathematician, astronomer and philosopher from Miletus, one of the seven wise men of Ancient Greece. His name is associated with the basic principles of geometry, such as the base and height, the angle between a straight line and a plane, the similarity of triangles.
4)Euclid is an ancient Greek mathematician, known as the author of The Elements, one of the first books on geometry. Recent research has shown that Euclid was not the only author of The Elements, and that the book was created over several generations of mathematicians.
5)Euclid is the name of the ancient Greek mathematician Euclid of Alexandria. His name comes from the Greek word "εὐκλείδης", which means "good glorified".
ОтветитьУдалить6)Indefinite terms in mathematics are terms that do not have a hard or unambiguous definition.
7) An axiom is a basic statement that is accepted without proof and is used to construct a mathematical theory.
A postulate is a statement that is accepted without proof within the framework of a certain theory.
A theorem is a statement that can be proved on the basis of axioms and postulates
8)They are needed to build a systematic and logical approach to solving mathematical problems and to substantiate mathematical conclusions.
9)Euclid's fifth axiom, also known as the axiom of parallel lines, states that if a straight line intersects two parallel lines, then the internal angles on one side are less than two right angles.
10)Geometry plays an important role in science, technology, engineering and design, as well as in everyday life, in addition, geometry contributes to the development of logical thinking and the ability to abstract thinking.
1) Geometry is used in many fields, including architecture, engineering, design, physics, computer graphics, and even in medicine and biology.
ОтветитьУдалить2)Geometry was passed on to the next generations through training courses in schools and universities
3) Thales is a ancient Greek philosopher and mathematician. His contribution to the development of geometry is that he was the first who proved that the circle is bisected by a diameter
4) New information about Euclid includes various aspects of his work: his contribution to the development of geometry, his work "Elements", his methods and approaches to the study of mathematics.
5) Euclid, an ancient Greek mathematician who lived in the III - II centuries BC, the author of "Beginnings", one of the most important works on geometry.
6) Underdetermined terms in geometry "point", "line" and "plane".
7) An axiom is a basic statement that is accepted without proof and is used to construct a mathematical theory.
A postulate is a statement that is accepted without proof within the framework of a certain theory.
A theorem is a statement that can be proved on the basis of axioms and postulates
8. All axioms, postulates and theorems are used for easier solving different kinds of problems in math
9. Euclid's fifth axiom states that if a straight line falls on two other straight lines and the interior angles on the same side are less than two right angles, then the two straight lines will meet on that side where the sum of angles is less than two right angles
10. Geometry helps us in improving different kinds of skills like logical thinking, deductive reasoning, analytical reasoning, and problem-solving
Габибов Акбар
ОтветитьУдалить1. Nowadays geometry is found everywhere, for example in nature, in space, in art and in architecture.
2. At this time old developments were passed down to the next generation without being discussed and proved.
3. Thales was the first mathematician who gave first known prove in geometry;
4. I obtained that in "Elements" was 13 chapters;
5. The Father of geometry. Because "Elements" contains almost everything which you can know about plane geometry and 3d figures;
6. In geometry, point, line, and plane are considered undefined terms because they are only explained using examples and descriptions;
7. Axioms or postulates are universal truths. They cannot be proved.Usually, postulates are used for universal truths in geometry, and axioms are used everywhere. Though, both mean the same thing. Theorem are statements which can be proved;
8. Axioms and postulates are used as the basis of proof. Theorems are needed to simplify the solution of problems in geometry;
9. If a line falling on two lines forms one-sided interior angles less than two lines in sum, then, extended indefinitely, these two lines will meet on the side where the sum of the angles is less than two lines;
10. Geometry gives not only an idea of the figures, their properties, relative position, but also teaches you to reason, ask questions, analyze, draw conclusions, think logically.
1. Today geometry is used in nature, space, art and architecture.
ОтветитьУдалить2. Geometric knowledge was passed on to the next generations without discussion and confirmation.
3. Thales is an ancient Greek scientist and mathematician who was the first to formulate and prove several geometric theorems.
4. According to new information from the video, it follows that Euclid taught mathematics in Egypt.
5. Euclid is known as the "father of geometry" because of his book "Elements", which includes 13 chapters on planimetry and volumetric geometry.
6. In geometry, there are vague concepts: a point, a straight line and a plane, which are explained only with the help of descriptions and examples.
7. An axiom is an unprovable statement; a postulate is a statement accepted without proof and refutable by experience; A theorem is a statement whose truth is proved mathematically.
8. They facilitate the introduction of concepts and help solve a variety of problems.
9. Euclid's 5th axiom states: "If a straight line passing through two straight lines forms internal angles smaller than two straight lines, then these lines will endlessly intersect on the side with smaller angles."
10. Geometry introduces us to the world around us, develops spatial thinking, introduces a variety of shapes and laws of their perception.
1) Currently, geometry is used in nature, space, art and architecture.
ОтветитьУдалить2) geometry passed on to the next generations without discussion or proof
3) Thales was a Greek mathematician who lived around 600 BCE and is considered one of the Seven Sages of Greece. His contribution to the development of geometry includes his theorem about the angles of a triangle, which states that the sum of the angles of a triangle is equal to two right angles.
4) New information suggests that Euclid was a mathematics teacher in Egypt
5) Euclid is called the "father of geometry" because he wrote a comprehensive treatise on geometry, called "Elements," which was used as a textbook for over 2,000 years.
6) In geometry, point, line, and plane are considered undefined terms because they are only explained using examples and descriptions;
7) In geometry, an axiom is a statement that is accepted as true without proof and is used as a basis for further reasoning and deduction. A postulate is a statement that is accepted as true without proof and is used as a basis for further reasoning and deduction. A theorem is a statement that can be proved from axioms and other theorems.
8) Axioms, postulates, and theorems are used in geometry to establish a logical framework for reasoning and deduction.
9) Euclid's fifth axiom states that if a straight line falls on two other straight lines and the interior angles on the same side are less than two right angles, then the two straight lines will meet on that side where the sum of angles is less than two right angles
10) Geometry helps us in improving different kinds of skills like logical thinking, deductive reasoning, analytical reasoning, and problem-solving
Юсубов Игит
1. Geometry is used in architecture, nature, art, etc.
ОтветитьУдалить2. geometric knowledge was passed on to subsequent generations without discussion or confirmation.
3. Thales is an ancient Greek scientist, philosopher and mathematician who was the first to formulate and prove several geometric theorems.
4. From the video it follows that Euclid taught mathematics in Egypt.
5. Euclid is known as the "father of geometry" thanks to his book "Elements", which includes 13 chapters on planimetry and solid geometry.
6. in geometry there are vague concepts: point, line and plane, which are explained only with the help of descriptions and examples.
7. axiom – an unprovable statement; postulate - a statement accepted without proof and refutable by experience; a theorem is a statement that has been proven mathematically to be true.
8. They help solve a variety of problems.
9. The 5th axiom of Euclid says: “if a straight line passing through two straight lines forms interior angles smaller than two straight lines, then these straight lines will intersect indefinitely on the side with smaller angles.”
10. geometry introduces us to the world around us, develops spatial thinking, introduces us to the variety of forms and the laws of their perception
Мамедагаев Саид
ОтветитьУдалить1. Currently, geometry is used in nature, space, art and architecture.
2. Geometry passed on to the next generations without discussion and confirmation.
3. he is the first mathematician to prove that a circle is bisected by its diameter.
4. From the video, I learned that Euclid was a mathematics teacher in Egypt. 5. Euclid's book, "Elements," is divided into 13 chapters and contains almost everything one needs to know about plane geometry, spheres, and other figures, which is why he is known as "the father of geometry."
6. A point, a line and a plane. They are considered as axioms in geometry
7. An axiom and a postulate are the statements are accepted to be true without any proof, but according to Euclid a postulate is more specific than an axiom. A theorem is a statement too, but it must be proven
8. axioms, postulates and theorems help us solve problems of all branches of geometry
9. Euclid's fifth axiom of parallel lines says that through a point that does not lie on a given line, only one line can be drawn parallel to the given line.
10. Geometry gives not only an idea of figures, their properties, relative position, but also teaches you to reason, ask questions, analyze, draw conclusions, think logically.