The mind map of the third grade mathematics circle summarizes the third grade mathematics circle: the definition of the circle is defined first.
The set of points whose distance from a fixed point on the same plane is equal to a fixed length is called a circle. This fixed point is called the center of the circle.
The length of a circle is the circumference of a circle. Two circles that can overlap are called equal circles.
A circle is a regular n polygon (n is an infinite positive integer), and its side length is infinitely close to 0 but can never be equal to 0.
The second definition
If the ratio of the distance between a moving point and two fixed points on a plane is equal to a constant that is not 1, then the trajectory of this moving point is a circle.
It is proved that the point coordinates are (x 1, y 1) and (x2, y2), the moving point is (x, y), and the distance ratio is k, which is derived from the distance formula of two points. Satisfy the equation (x-x 1) 2+(y-y1) 2 = k 2 * [(x-x2) 2+(y-y2) 2] When k is not1,a cyclic equation is obtained.
Geometric method: Assuming that the fixed points are A and B and the fixed point is P, it satisfies |PA|/|PB| = k(k? 1), the intersection point p is the bisector of the inner angle and the outer angle of the angle APB, and intersects with the extension lines of AB and AB at C and D, and the angle CPD=90? . From the angle bisector theorem: PA/PB = AC/BC = AD/BD =k, it is noted that the positions of C and D are unique. C is on the line segment AB, D is on the extension line AB, and for all P, P is on the circle with the diameter of CD.
Mathematics circle of grade three: related definition diameter
1. The line segment connecting the center of the circle and any point on the circle is called radius, and the letter is expressed as r (radius).
2. The line segment whose two ends pass through the center of the circle is called diameter, and the letter is expressed as D (diameter). A straight line with a diameter is the symmetry axis of a circle.
Diameter of circle d=2r
bowstring
1. A line segment connecting any two points on a circle is called a chord. The longest chord in the same circle is the diameter. The straight line with the diameter is the symmetry axis of the circle, so there are countless symmetry axes of the circle.
arc
1. The part between any two points on the circle is called arc, or arc for short. ⌒? Express delivery.
2. The arc larger than the semicircle is called the optimal arc, and the arc smaller than the semicircle is called the suboptimal arc, so the semicircle is neither the optimal arc nor the suboptimal arc. The optimal arc is generally represented by three letters, and the suboptimal arc is generally represented by two letters. The optimal arc is an arc with a central angle greater than 180 degrees, and the suboptimal arc is an arc with a central angle less than 180 degrees.
3. In the same circle or equal circle, two arcs that can overlap each other are called equal arcs.
corner
1. The angle of the vertex on the center of the circle is called the central angle.
2. The angle where the vertex is on the circumference and both sides intersect with the circle is called the circumferential angle. The angle of a circle is equal to half the central angle of the same arc.
circumference ratio
The ratio of the circumference of a circle to the length of its diameter is called pi. It is an infinite acyclic decimal, usually represented by letters, = 3.1415926558972384626. 3. 14 is generally needed for calculation. We can say that the circumference of a circle is the diameter. Times, or about 3. 14 times, can't directly say that the circumference of a circle is 3. 14 times the diameter!
shape
1. The figure surrounded by the chord and the arc it faces is called an arch.
2. The figure enclosed by two radii of the central angle and an arc corresponding to the central angle is called a sector.