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Pobudova correct bagatokutnik_v - technical armchair. Pobudova correct bagatokutniks Pobudova 8 kutnik

The chair most often needs to be positive. So, say, positive octagons zasosovyutsya on the boards of road signs.

You know

  • - compass
  • - line
  • - olivets

Instructions

1. Let the tasks come from, rivny dovzhiny on the side of the bazhany eight-cutter. It is necessary to play a new eight-way school. With the first crochet, induce the tricytnik to a given length of time, stagnate in a given way, as before. For a whole lot of comprehension, encourage the square from the side, so that it can be drawn in a new diagonal. Infect the bisector bisectors at the diagonals (on the smallest bisectrix the blue is indicated), on the cross bisectors the vertex is set tricycle tricycle, Sides of the same level of radius of the stake, described near the correct eight-mile.

2. Indulge in the center at the top of the trikutnik. radius cola road side trikutnik. Infect the compasses for the size equal to the value of the given size. Add the price to the number of repairs from any end of the process. Ob'nayte all otrimanі points in the eight-kutnik.

3. If the circle is set, the eight-kutnik is guilty of the inscriptions, then encourage it to be even simpler. Encourage two lines perpendicular one to one to pass through the center of the stake. On the peretin_ axials of that kola, one can see the chotiri tops of the maybutny eight-kutnik. The overflowing podіliti appears between the dots on the dusi cola navpіl, and then trim off some of the summits.

virniy trikotnik- the one that all sides have an identical pre-genie. Vyhodyachi z ts'go viznachennya, pobudova podbnoy izvody trikotnik a є don't care about employees.

You know

  • Liniyka, sheet of paperwork, olivets

Instructions

1. Take an arkush of a clean paper, distributed in a wall, a line and a pidmitity on a paper three points, so that the stench was on the identical appearance one of one (Fig. 1)

2. With the help of a line, one by one, one by one, it is shown on little 2.

Brutal respect!
In a virny (rivnobichny) tricycle, all kuti is equal to 60 degrees.

Korisna is happy
An equilateral tricycle so it is very equable. As a trikutnik of equestrianism, then tse means, scho 2 from 3-rd sides, and the third party is entered upon. Any positive tricycle is not correct at that hour.

eight-way- tse, according to its essence, two squares, one for one at 45 ° and one on the top of the whole line. And for that, in order to positively depict such a geometric figure, we need to repeat the olives hefty hefty, according to the rules to make a square, or to carry out offensive actions. Viklad is oriented to the side, but the road is 20 cm. And that means, when the chair is folded out, look, the vertical and horizontal line of the 20 cm was placed on the arch paper.

You know

  • Linijka, rectangular tricycle, protractor, olivets, compasses, arkush paperu

Instructions

1. Method 1. Place a horizontal line at the bottom with a length of 20 cm. When you write from one side, use a protractor to use a straight edge, the one in the warehouse 90 °. The same can be done with pidtrimkoy direct tricycle... Draw a vertical line and respect 20 cm. Make the same manipulation from the other side. Add two points with a horizontal line. As a result, I went geometric figure- square.

2. In order to make the 2nd (replacement) square, you need the center of the figuri. For the sake of subdividing the side of the square into 2 parts. Combine a set of 2 points of parallel upper and lower sides, and then points of the side sides. Draw 2 straight lines through the center of the square, perpendicular to each other. Repairing from the center, see on new straight lines up to 10 cm each, so as a result you will give 4 straight lines. Combine 4 otrimanі zovnіshnі points between yourself, as a result of which you will see the 2nd square. Infectious be-a point from 8 otrimani kutіv, take care of yourself. In this rank, an eight-kutnik will be seated.

3. Method 2. For all, you will need a compass, a line and a protractor. Towards the center of the arkush from the side of the compass, place it about 20 cm in diameter (radius 10 cm). Draw a straight line through the central point. Send a friend to a perpendicular line. The same can be done with the help of a protractor or a straight tricycle. As a result, there will be a number of changes for 4 parts. Distant leather from sections are divided into 2 parts. For others, it is also possible to speed up with a protractor, at 45 ° or rectangular tricycle That is, to put a gostry kut at 45 ° and to carry out an exchange. Go to the center on a straight line, look at 10 cm. As a result, you will see 8 promises, which will help you. We have an eight-kutnik in the bag.

4. Method 3. For a person, place the colo on its own, draw it through the middle of the line. When you play the protractor, put it in the center and see the cut, look out, but every section of the eight-walk can be in the center of the cut 45 °. Consider a 10 cm dinner for the least on otrimannyh interchanges. eight-way ready.

Korisna is happy
Robbing the chair is a solid olivist, a bit of a line on any writing can be easily seen

Virny eight-kutnik is a geometrical figure, for which every kut should be 135?, And all sides between themselves are equal. Tsia figura is very often victorious in architecture, for example, when the columns are up, as well as when the road sign STOP is made. Yak is namalyuvati a positive eighth-grade student?

You know

  • - album arkush;
  • - olіvets;
  • - line;
  • - compasses;
  • - eraser.

Instructions

1. Paint a square with the spatula. Try to hold the stake so that the square is resting in the middle of the stake. Infect the two axes of the middle line of the square - horizontally and vertically until they cross the stake. Add straight lines to the points of the overflow of the axes with a stake and points to the described stake with a square. In such a rank, cut off the side of the virgin eight-kutnik.

2. Paint the vіrniy eight-kutnik with the іnshim method. Spread over a colo. In order to draw a horizontal line through the center. Respect the overflow point of the extreme right border of the column from the horizontal. The point will be the center of more than one number, with a radius equal to the front of the figure.

3. Draw a vertical line through the overflow points of the 2nd circle from the front. Place the lower compass at the point of the vertical cross-strand from the horizontal and place a small radius with a small radius, equal to the center of the crooked circle to the center of the cob stake.

4. Attach a straight line through two points - the center of the cob stake and the point overflowing the vertical and the crisp circle. Continue until the crossing with the cordon of the cob figuri. Tse will be the point of the top of the eight-track. Use a compass to respect one point, having held the spike in the center at the point, overturning the extreme right cordon of the cob cola from the horizontal and radius, equal to the center to the top of the eight-track.

5. Draw a straight line through two points - the center of the cob stake and the last point. Continue the straight line until the overflow between the interiors of the primary figurines.

6. Combine with straight lines in a common way: the point of the horizontal overflow from the right cordon of the cob figur, writing for the year-round arrow, all the points were set, including the point of overflow of the axes from the primary circumference.

Video by topic

Pobudov inscribed in the colo of the correct six-walk. Pobudova shestikutnik zasnovane on the one side of the road to the radius of the described stake. That is, in order to induce a sufficient distribution of the circle into a number of rural parts and know the points between themselves (fig. 60, a).

The correct six-walk can be done by using a 30X60 ° flight. For a clear cut, induce a horizontal diameter of the circle for the bisector of the cuts 1 and 4 (fig. 60, b), it will be right on the side 1 -6, 4-3, 4-5 and 7-2, if it is carried out on the side 5-6 and 3 2 ...

Pobudov inscribed in the color of the equilateral trikutnik... The tops of such a tricycle can be followed by an additional compass and a pair of kutas at 30 and 60 °, or only one compass.

There are two ways to induce the one-sided tricycle inscribed in the color.

first way(Fig. 61, a) on the fact that all three kutis of the tricut 7, 2, 3 are located at 60 °, and a vertical straight line is drawn through point 7, є at once by the height and bisector kut 1. So yak kut 0-1- 2 roads 30 °, then for the known side

1-2 to finish staying on points 1 and sides 0-1 cut at 30 °. For the whole, I will set up the flight and cosine so, as shown in the figure, carried out by the line 1-2, as there will be one side of the shukany tricycle. After reaching side 2-3, I will put the race in the position shown by the dashed lines, and through point 2 it is drawn straight, as to designate the third top of the tricycle.

other way for the reason that you will stay correct six-walker, Inscriptions in a number, and then from one summit through one, then we see an equilateral trikutnik.

To induce the tricycle (fig. 61, b), the diameter of the apex-point 1 is indicated and a diameter line 1-4 is carried out. Distant from point 4 with a radius equal to D / 2, an arc can be described up to overflowing with a stake at points 3 and 2. Otrimanі points will be two іnshih tops of a shukany tricycle.

Pobudova square, inscribed in a colo... Tse pobudova can be a visonati behind the help of a kutnik and a compass.

The first way of filing is on the fact that the diagonal of the square is overturned in the center of the described stake and up to the axis of 45 °. On the way out, I will install the races and skirts with 45 ° cuttings so, as shown in fig. 62, a, і point 1 і 3. Distances through the points are drawn behind the additional flight line of the horizontal sides of the square 4-1 and 3-2. Then, behind the help of the flight, along the leg of the kutnik, the squares 1-2 and 4-3 are held vertically to the side.

Another way of fixing on the fact that the vertices of the square move around the arc of a circle, linking between the edges of the diameter (fig. 62, b). There are two mutually perpendicular diameters of points A, B and C at the ends of the circle, with a radius at the described arc to a mutual overflow.

Distant through the points of the overflow of the arcs is carried out in additional straight lines, as seen on the figures by means of suction lines. Points їх will cross with a stake and start vertices 1 and 3; 4 and 2. Otrimanі with such a rank the tops of the shukany square are given the same last time.

Pobudov inscribed in the colo of the correct p'yatikutnik.

Schedule to enter the correct five-kutnik into the colo (fig. 63).

Namichaєmo on the number of point 1 and take place for one of the peaks of the five-kutnik. Dilimo vidrizok AT navpil. For a number of radius AT from point A, an arc can be described up to overflow with a stake at points M and B. Having found the points of a straight line, we can see point K, as we move from point 1. With the help of a radius, we will move along the front of A7, and describe the arc up to point A7. from the diameter line AT at point H. Having found point 1 from point H, we can see the side of the pentacute. With the help of the compass, we cut 1H, describing the arc from the vertex 1 to the overflow with the stake, we know the vertices 2 and 5. Having cut the notches from the vertices 2 and 5 with the same diameter of the compass, we can recognize the three vertices 3 and 4. The known points from the last yourself.

Pobudova of the correct p'yatikutnik according to the tribute of the third party.

To induce the correct five-year-old according to the tribute of the thirteenth side (fig. 64) dimo from AB to the whole of the rural parts. From points A and B in radius AB, an arc is described, which overflows to give point K. Through point і rose 3 on straight line AB, a vertical straight line is drawn.

Otrimaєmo point 1-the top of the p'yatikutnik. Then, by radius, equal AB, from point 1, an arc can be described to overflow with arcs, previously drawn from points A and B. The points of overflow of arcs start the tops of the pentacle 2 and 5. Know the peaks once again.

Pobudov inscribed in the correct seven-walker.

Let the circumference of diameter D be given; it is necessary to write in the wrong seven-turn (fig. 65). Dimo is the vertical diameter of the circle on seven equal parts. From point 7 in radius, equal to the diameter of the circle D, an arc is described up to the overflow with the extended horizontal diameter at point F. Point F is called the pole of the bagatokutnik. Having reached point VII for one of the peaks of the seven-yoke, it is carried out from the pole F through the pair of the vertical diameter of the promenade, which overflows from the circumference to the beginning of the peaks VI, V and IV of the seven-yoke. To detach the peaks /// - /// from points IV, V and VI, it is carried out to cross-over with a stake of horizontal straight lines. Know the peaks once and for all. Seven-yards can be prompted by a way to carry out changes from the pole F through an unpaired sub-line of the vertical diameter.

Guidance is a useful way to induce the right bagatokutniks with any number of sides.

Podil cola on the be-yak, the number of parts can be carried out in the same way, according to the data in the table. 2, in which functionality has been established, which gives the possibility of starting a change of sides of the correct inscribed bagatokutniks.

Kuklin Oleksiy

Robot wearing abstract character with elements prelude to business... They look at them different ways encourage the correct n-kutniks. The robot will have a lecture on the nutrition about those who, as soon as possible, can spend the n-kutnik behind an additional compass and line. The robot will be given a presentation, as you can see on this mini-site.

Zavantazhiti:

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Front view:

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Signatures before slides:

Pobudova correct bagatokutnik_v Robot vikonav: student of the 9th grade "V" MBOU ZOSH No. 10 Kuklin Oleksiy

Correct bagatokutniks A regular polygon is called a bulbous bagatokutnik, which has all sides and kuti ryvn. Go to the butt of the opuque bagatokutnik is called the bagatokutnik, all the specks of which lie on one side of the way, be it straight, but pass through the two sides of the peaks.

Back Correct bagatokutniki

The pioneers of the mathematics section about the correct bagatokutniki bouli davnogretski vcheni. Some of them are the boules of Archmed and Evklid.

Proof of the correct n-kutnik Yaksho n (the number of kut_v bagatokutnik) is more than 2, then such kutnik is іsnu. I will try to spend 8 kutnik and bring the price. Dovedennya

At the same time, there are 8 arcs in the center at the point of O. Rozdilimo and the number of arcs in our range is 8. For the whole we have carried out a radio, so that there were 8 arcs; 8), similarly to the skin length at 45 °.

3. The points A1, A2, A3, A4, A5, A6, A7, A8 can be recognized. By the way, we will recognize the correct eight-mile. back

Pobudova of the correct bagatokutnik on the sides from the victorian turn. The correct bagatokutnik can be found if you know your kuti. We know that the sum of the kutiv of the opukly n-kutnik is up to 180 ° (n - 2). You can count the bagatokutnik kut by distributing the sum by n. kuti Pobudova

Correct cut: 3-walk for the road 60 ° 4-walk for the road 90 ° 5-walk for the road 108 ° 6-walk for the road 120 ° 8-walk for the road 135 ° 9-walk for the road 140 ° 10-walk for the road 144 ° 12-walk for the road ° Degree world of kutіv correct trikutnikіv Back

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Signatures before slides:

In 1796, Karl Friedrich Gaus, one of the best mathematicians in all hours, showed the ability to induce correct n-kutniks, as well as to show the equality, de n is a number of kutiv, but k-be as natural. Tim himself saw it, in the middle of 30 he could put a stake into 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30 parts. In 1836, the rotsi Wantsel didn’t, but the correct bagatokutniki, but they didn’t give the rationality for an additional line and compass, couldn’t be kept. Gauss's theorem

Pobudova trikutnik I will stay with the center at point O.

3. Z'є цент Back Pobudova trikutnik

Pobudova shestikutnik 1. Wake up the stake with the center at point O. 2. Draw a straight line through the center of the stake. 3. Draw an arc of the circle of the same radius with the center at the point overflow straight from the stake to overflow into the stake.

4. Draw a straight line through the center of the cob circle and the point to cross the arc with a circle. 5. Z'є pobudova shestikutnika

Pobudova chotirikutnik I will stay with the center at point O. We will carry out 2 mutually perpendicular diameters. From points in which diameters the circle is carried out by the same circle of the given radius up to the cross-section (kil).

Pobudova chotirikutnik 4. Conducted straight through the points of overflow kil. 5. Z'є

Pobudova eight-kutnik You can be a regular bagatokutnik at someone 2 times more kut_v than a given one. I'll stay for an eight-kutnik for the help of a chotirikutnik. One of the opposite peaks of the chotirikutnik. Conducted by the bisectrix of the kutiv approved by the pereichny diagonals.

4. Z'єdnaєmo points lie on scho koli, otrimavshi at tsomu vosmikutnik correctly. Pobudova eighth-grade student

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Signatures before slides:

Pobudova decagonism I will stay with the center at point O. We will carry out 2 mutually perpendicular diameters. Rozdilimo radius cola navpil and from the rim to a new point, a circle is drawn to pass through point O.

Pobudova decagonism 4. Draw from the center of a small circle to a point in a large circle to reach its radius. 5. From the point of the dot to the great stake and the radius, we will carry out the circle so that you will stick with the little one.

Pobudova decagon 6. From the point of crossing the great і і і і іrіmanoі kіl carried out, the stake was prompted in the last time and so we will carry it out until the quiet time until the suspension begins to stick. 7. Z'є

Pobudova p'yatikutnik To induce the correct p'yatikutnik, it is necessary for an hour to induce the correct decagonism from all points, but through one.

Approximately the pobudova of the correct penticut by the method of Dürer I will motivate 2 stakes to pass through the center of one of one. Z'єdnaєmo center the straight, having cut off one of the sides of the penticut. Z'є

Approximately pobudova correct p'yatikutnik by the method of Dürer 4. Carrying out one more radius with the center at the point of overturning two lines. 5. Conducted 2 vidrizka yak is assigned to the baby.

Approximately the induction of the correct pyatikutnik by the method of Durer 6. The same point to the dots of tsikh vіdrizkіv with kolami with knots prompted the side of the pyatikutnik. 7. Dobuduєmo to five-kutnik.

Approximate Pobudova Correct Petykutnik by the methods of Kovarzhik, Bion

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