Actively and fun to shoot the game "Dangerous weapons". How clear from ...
From the history of history, the right polygons were known in ancient times. In the Egyptian and Babylonian antique monuments there are regular quadrangles, hexagons and octagons in the form of images on the walls and decorations, carved them by their stone. Ancient Greek scientists began to show a great interest in the right polygons since the times of Pythagora. The doctrine of the correct polygons was systematized and set out in the 4th book "Beginning" Euclida.
Right polyhedra of Platonov Body: Tetrahedron - "Fire" Cuba- "Earth" Octahedron - "Air" Dodecahedron - "The whole world" Ikosahedron - "Water"
Proper polygons In nature, the correct polygons in nature are the right polygons are found in nature. One example is bee honeycomb, which are a rectangle covered by proper hexagons. On these hexagons, the bees are grown from the wax cell, which are direct hexagonal prisms. In them, bees and laying off honey, and then re-coated with a solid rectangle from wax.
Sources of information: children's encyclopedia "I will know the world" Mathematics, Moscow, AST, 1998. ru.wikipedia.org/wiki/ History of Mathematics A..I. Azevich Twenty Machines Harmony: Humanitarian-Mathematics Course. - M.: School Press, 1998.
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Right polygons (geometry grade 9) Volodina N.L.
Objectives of the lesson: 1. Recover the concept of a polygon, the formula of the sum of the angles of the convex polygon. 2. To know with the right polygons, teach to build the right polygons. 3. Place the task solutions on the topic.
Oral questions: 1. What is the sum of the angles of the convex polygon? (N - 2) ∙ 180 ⁰ 2. How to find one hexagon angle if all the corners are equal? (6 - 2) ∙ 180 ⁰ / 6 \u003d 120⁰ 3. How to find an angle of n-cart, if all the angles are equal? (n - 2) ∙ 180 ⁰ / n
What is the sum of the corners of the triangle? 180 ⁰
The sum of the angles of the polygon 1. What is the sum of the angles of the convex four-broth? 360 ⁰ 2. What is the sum of the angles of the convex hexagon? 720 ⁰
Divide polygons into two groups
Right polygons arbitrary polygons
Definition: Convex polygon is called correct if it all sides are equal and all corners are equal
The correct triangle is equilateral triangle all sides are equal. All corners of 60.⁰
The right quadriller square all sides are equal. All angles of 90.⁰
The right pentagon all sides are equal to all angles of 108⁰
Proper hexagon All parties are equal to all angles of 120⁰
Final Questions: 1. How is a polygon called correct? 2. Does the correct 10-square cover? 20-square? 3. How to build a regular polygon?
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Lesson on the topic "Right polygons"
Objectives lesson:
educational:introduce students with the concept and species of the right polygons, with some of their properties; teach the use of the formula to calculate the corner of the correct polygon
- developing:
- educational:
Lesson:
1. Organizational moment
The motto of the lesson:
Three ways lead to knowledge:
Chinese philosopher and sage of confusion.
2. Motivation of the lesson.
Dear Guys!
I hope that this lesson will be wondering, with great benefit for everyone. I really want those who are still indifferent to the queen of all sciences, from our lesson left with a deep conviction that geometry is an interesting and necessary subject.
French writer XIX century Anatole France once remarked: "You can only learn fun ... To digest knowledge, you need to absorb them with appetite."
Let's follow the advice of the writer at today's lesson: be active, attentive, absorb with a great desire of knowledge that you will find in your future life.
3. Actualization of reference knowledge.
Frontal survey:
What are their elements?
Types of polygon
4. Studying a new material.
Among the many different geometrical figures on the plane there is a large family of polygons.
The names of geometric shapes have a completely definite meaning. Look carefully by the word "polygon", and tell me which parts it consists. The word "polygon" indicates that all the figures of this family "many corners".
Submold to the word "polygon" instead of a "a lot of" part specific number, for example. 5. You will receive a pentagon. Or 6. Then the hexagon. Notice how many corners, so many sides, so these figures could well be called multilaterals.
In the figure, geometric shapes. Using the drawing, name these figures.
Definition. The correct polygon is a convex polygon, in which all the corners are equal and all sides are equal.
With some correct polygons, you are already familiar - an equilateral triangle (correct triangle), a square (right quadrangle).
We will get acquainted with some properties that all right polygons possess.
The sum of the angles of the polygon
n - number of parties
n-2 - the number of triangles
The sum of the angles of one triangle - 180º, multiply by the number of triangles N -2, we obtain S \u003d (N-2) * 180. 
S \u003d (N-2) * 180
Formula for calculating the angle x of the correct polygon
.
Bring the formula to calculate the angle x of the correct N-Cornel.
In the right polygon, all corners are equal, the amount of the angles is divided by the number of angles, we obtain the formula:
x \u003d (n-2) * 180 / N
5. Fastening a new material.
Solve № 179, 181, 183 (1), 184.
Without turning the head, circle the wall of the class around the perimeter clockwise, the cooling board around the perimeter counterclockwise, the triangle depicted on the stand clockwise and an equal triangle counterclockwise. Turn the head to the left and look at the horizon line, and now on the tip of your nose. Close your eyes, count to 5, open your eyes and ...
We put my palm to the eyes,
Legs strong lay.
Turning to the right
Looking too much.
And should be left too
Look out from under the palm.
And - right! And further
Through the left shoulder!
and now continue to work.
7. Independent work of students.
Solve No. 183 (2).
8. Camera lesson. Reflection. D / s.
What do you remember most about the lesson?
What surprised?
What did you like most?
How do you want to see the next lesson?
D / s. Learn paragraph 6. Solve № 180, 182 185.
Creative task:
Internet :
View the contents of the presentation
"Right polygons"
- - educational: introductory students with the concept and species of the right polygons, with some of their properties; Teach use the formula to calculate the corner of the correct polygon
- - developing: The development of cognitive activity, spatial imagination, the ability to choose the right decision, concisely express their thoughts, analyze and draw conclusions.
- - educational: Education of interest in the subject, the ability to work in the team, culture of communication.
The motto of the lesson:
Three ways lead to knowledge:
The way of reflections is the path is the most noble;
The path of imitation is the easiest way;
The path of experience is the path is the most bitter.
Chinese philosopher and sage
Confucius.
- What geometric figures have we already studied?
- What are their elements?
- What figure is called a polygon?
- Types of polygon
- What is the perimeter of a polygon?
- What is the sum of the internal angles of the polygon?
Wrong correct polygons
- The convex polygon is called correct if he has all the corners equal and all sides are equal
Properties of correct polygons
Amount corners
polygon
n is the number of sides of N-2 - the number of triangles The sum of the angles of one triangle is 180º, 180º multiply by the number of triangles (N -2), we obtain S \u003d (N-2) * 180.
Formula for calculating the corner of the correct p - Galla
In the right p - Galnik all corners are equal, the amount of the angles is divided by the number of angles, we obtain the formula:
but n. \u003d (N-2) * 180 / N
Test Select the correct approval numbers.
- The convex polygon is correct if all of its parties are equal.
- Any correct polygon is convex.
- Any quadrangle with equal parties is correct.
- The triangle is correct if all its corners are equal.
- Any equilateral triangle is correct.
- Any convex polygon is correct.
- Any quadrangle with equal corners is correct.
Independent work
but p \u003d (N-2) * 180 / N
but 3 =(3-2)*180/3= 180/3= 60
Homework
№ 1079 (orally), No. 1081 (B, D), № 1083 (b)
Creative task:
* Historical certificate of correct polygons. Possible requests for the search engine network Internet :
- Polygons at Pythagorean School. Building polygons, Euclid. Right polygons, Claudius Ptolemy.
- Polygons at Pythagorean School.
- Building polygons, Euclid.
- Right polygons, Claudius Ptolemy.
