Yak porahuvati part of the dojini stake. Formulas for the area of the stake sector and for the first arc
Colom I call a closed, flat curve, all the points that are near the same area, visible from the same points from the center.
Speck About є center stake, R є By the radius of the stake - I will go from the point of the stake to the center. For the value of a closed radio
Small. 1
curves may, however, be the same kind of dinner.
Vidstan between two stake points is called a chord. The tip of a stake, which passes through the center and the two points, is called a diameter. The middle of the diameter is the center of the stake. The stake points extend into a closed curve on two parts, the skin part is the arc of the stake. As soon as the end of the arc is to fit the diameter, then it is also called a pivkol, which is taken to mean π ... Degree turn is two years, which may turn into 360 degrees.
Concentric cola - the cola, which may be the main center. Orthogonal cola - a cola, which is re-swayed up to 90 degrees.
Ploshchina, the yak will be surrounded by a stake, called a stake. One part of a stake, a yak is surrounded by two radii and an arc - a whole circular sector. The arc of a sector is a chain arc that will surround the sector.
Small. 2
Instead, rostashuvannya stake that straight (Fig. 2).
The circumference and straight line are two sleeping points, which go straight ahead to the center of the mensha stake behind the radius of the stake. In such a way, it is straightforward to call it a cola.
The surroundings and straight lines go to one corner point, so that you go straight ahead to the center of the stake to the radius of the stake. At such a time, it is straightforward in terms of delivery to the stake to be called dota to the stake. ЇKhnya zagalna point to wear I’ll name the point dotsiku kola і straight.
Basic cola formulas:
- C = 2πR , de C - more girth of the circumference
- R = C / (2π) = D / 2 , de З / (2π) - Dovzhina arc stake
- D = C / π = 2R , de D - Diameter
- S = πR2 , de S - cola area
- S = ((πR2) / 360) α , de S - The area of the circular sector
Kolo and Kolo took their name from the Ancient Greece. Already in the old days, a man was tricked into a round body; Those that were so round could collapse by themselves, became a shipment to the wine-wheel of the wheel. Would you like to be so special? Ale to understand, as in one mile of a wheel to learn from our life. Nadal tsei vinakhid gave rise to the mathematical understanding of the stake.
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Colo, yogo parts, їх development and communication - speeches, with which jewelry is permanently stuck. Kiltsya, bracelets, casts, pipes, coolers, spirals - a lot of all round robots. How is it that all the time is porahuvati, especially how you spared the school to skip the lessons of geometry?
Let's take a look at how it smelt parts and how it stinks.
- Kolo - lіnіya, scho I will surround the colo.
- The arc is a part of the stake.
- Radius - vidrizok, which is the center of the stake, as a point of the stake.
- Horda - from the point of the stake.
- The segment is a part of the stake, surrounded by a chord and an arc.
- The sector is a part of the stake, surrounded by two radii and an arc.
The magnitude that will cite us is the same value:
Now, as a matter of fact, as a zavdannya, tied with pieces of stake, it is brought to virishuvati.
- To know the end of the rosigorta, be it a part of the ring (bracelet). Assignments diameter and chord (option: diameter and central cut), know the arc's length.
- Є little ones in the area, you need to know about their size in the projection of the letter in the arc. Set the arc and the diameter, know the jordi.
- Diznat the visota of details, otrimanoy zginannyam flat workpieces in an arc. Variants of vykhidnykh danikh: additional arc and diameter, additional arc and chord; Visually the height of the segment.
Life, even if only for the first time, but I don't have to, in order to show the need for a set of two parameters for the knowledge of all of them. The axis of the tsim mi will be occupied. And itself, there are five parameters of the segment: D, L, X, φ and H. Potentially, you can bet on them, you can bet on them, and by the way of the brain storm all the people know.
I’m not going to give the reader any advice, I won’t guide the lecturer's decisions, but I’ll guide the results in the formulas (ie, there is no formal solution, I’ll discuss it along the way).
One more respect: about one vimira. All sizes, except for the central kut, are immersed in the quiet, abstract ones themselves. It means that if, for example, you set one value in millimeters, then I don’t need to set it in centimeters, but the resulting value is in quiet millimeters (and the area is in square millimeters). The same can be said about inches, feet and sea miles.
I only the central kut depends on the degree and not the least. That is why, as the practice shows, people who design more round, are not shy in the radio. The phrase “kut pi na chotiri” should be put at the deaf kut, tody yak “kut forty five degrees” - zoosulya everything, oskil tse all five degrees is more for the norm. However, all formulas will have an intermediate value of more than one cut - α. Behind the zmіstom, half of the central kuta, vimіryana in radіans, even in tsei sense, you can calmly not grasp.
1. Given diameter D and length of arc L
; dojina jordi 
;
segment height 
; central kut 
.
2. Dani diameter D and dovzhina chordi X
; arc dovjina;
segment height ; central kut 
.
Oskіlki chord dіlit colo into two segments, the price is not one, but two decisions. Schob otrimatie to each other, it is necessary to use the formulas pointing in the direction to replace the cut α on the cut.
3. Given the diameter D and the central cout φ
; arc dovjina;
dojina jordi ; segment height .
4. Dany diameter D and height of segment H
; arc dovjina;
dojina jordi ; central kut .
6. Given the arc L and the central cout φ
; diameter;
dojina jordi ; segment height .
8. Given a chordi genius X and a central cout φ
; dogina arc 
;
diameter; segment height .
9. Dany of the chordi X and the height of the H segment
; dogina arc ;
diameter; central kut .
10. Given the central cut φ і height of the segment H
; diameter 
;
arc dovjina; dojina jordi .
Dear reader, I don’t think I’m missing two options:
5. Given an edge of an arc L and an edge of a chordi X
7. Dany of the arc L and the height of the H segment
There are two irrelevant issues, if there is no solution, it is possible to write down the formulas at the viewer. And the zavdannya is not the same anyway. For example, you є have a flat preparation of the L-level and you want to bend it, so that the new-generation became X (or the height became H). What diameter should you take the frame (crossbar)?
The zavdannya price is to be raised before the razvyazannya ryvnyan: 
; - for option 5
; - Variant 7
I want the stench not to be scanned analytically, the protest is easy to scan in a programmatic way. And I know how to take this program: on the site itself, for the first time. All those who I’m about to tell you can do it in a microsecond.
To expand the picture of the dodamo to the results of ours, count up to the number of the stake and three values of the area - stake, sector of that segment. (We can help even when calculating the mass of all round and round details, but even in the approximate statistics.)
additional circumference;
cola area 
;
sector area 
;
area of the segment 
;
Once again, I’ll guess again about the idea of absolutely no-brainer programs, as a vison of all the re-insurance of the calculation, you are aware of the need for zgaduvati, which is also the arctangent and de yogo shukati.
Here's how:
Malunok 463.1... a) the arc is obvious; b) the value of the dojini chordi of the ta visoti segment.
In such a rank, if є an arc, we can recognize the chord of the head L. In the middle of the chord, we can draw a line perpendicular to the chord, and with such a rank we can recognize the height of the segment H. Now, I know the chord, the chord of the segment visually the central kut α, tobto. cut with radii, holding from the cob that end of the segment (not shown on the little 463.1), and then the radius of the cola.
The revision of the submission to the end of the report was seen at the statti "Rozrahunok of the arched bridge", so here I will deprive you of the basic formulas:
tg ( a/4) = 2H / L (278.1.2)
a/ 4 = arctg ( 2H / L)
R = H/ (1 - cos ( a/2)) (278.1.3)
Yak Bachimo, I will look at the mathematics of current problems due to the significance of the radius of the stake. The Danish method allows the value of the radius of the arc to be accurate. The price is a bit overwhelming to the method.
And now let's talk about the shortcomings.
The problem with the given method is not in the fact that it is necessary to memorize the formula for the school course in geometry, but it has been successfully forgotten in that - in order to find the formula - the Internet. And the axis is a calculator with the functions arctg, arcsin and ін. є far from the skin corystuvach. I want the problem to be also successfully allowed by the Internet, but do not go to oblivion, which can be done by the application. Tobto. It is far from being required that the radius of the stake is greater with an accuracy of up to 0.0001 mm, an accuracy of 1 mm can be quite acceptable.
In addition, in order to know the center of the stake, it is necessary to advance the height of the segment and the power to the most direct distance, to the right distance. So, as in practical situations I can right with not ideal vimiruvalny attachments, until the next time I can tweak when growing, go, but less than the height of the segment according to the date before the jordi, it’s more possible to tweak the center.
I know how to forget about someone who is not an ideal vipadok, tobto. tse mi so at once called the curve arc. As a matter of fact, it can be crooked, but it can be described to finish with a foldable mathematical deposit. And the knowledge of such a rank is the radius that the center of the stake can be, and not back to the actual center.
I want to propose one way to get the radius of a stake, which I myself often criminate, which is the way to get a radius of a stake more and more simply, I want the exactness of a meaning less.
Another method of measuring the radius of the arc (method of last-minute approach)
Also, the view of the obvious situation is continuing.
So, as we all need to know the center of the stake, then for the cob from the points, the cob and the end of the arc are drawn as a minimum of two arcs to the radius. There will be a straight line through the peretin tsikh of the arcs, on the yak there is the center of the shukany stake.
Now, it is necessary to make a repetition of the arcs from the middle of the chordi. However, since the values of the points are carried out not along one dozen, but along two, then a straight line passes through the intersection of these arcs and the middle of the chords is not necessary.
When the arc is seen from the arcs to the cob, or the end of the arc, so that you can see more, below the arches are seen to the point where you can see the height of the segment, then the center of the arc is seen to be located lower on the straight line. Yaksho menshe - that shukaniy the center of the arc is directed to the straight.
To that, the offensive point is straight ahead, which is directly visible to the center of the arc, and from where it is violated. Possibility to approach the offensive point and then repeat itself. With a new point of skin, growth will be deed by menshoy.
Axis, vlasne, and everything. Do not be astonished at the simple and folding descriptions, for the radius of the arc to be measured in this way with an accuracy of up to 1 mm, 1-2 chilines are enough.
Theoretically, the tse view is approximately like this:
Malunok 463.2... Viznachennya to the center of the arc by the way of the last day.
And in practice, approximately like this:
Svitlina 463.1... Razmіtka billet of folding form іznіymi radіuses.
Here it is only for the time being, as soon as it happens that we know that chick of radios, that on the photograph it’s so rich in everything.