圆是平面形状吗?
几何是一门数学学科,研究平面形状和实体形状及其属性和表示方式。根据几何的标准定义,它是对形状、结构、它们的大小、形成的角度和表示的研究。欧几里得被公认为几何之父。该研究解释了平面形状(如圆形、三角形、正方形、矩形等)和实体形状(如球体、圆柱体、圆锥体、立方体、长方体等)的性质。
平面形状
平面是一个平面的二维表面,延伸两个无穷大并且没有高度。并且,在这些平面上表示的有界二维图形称为平面形状或平面形状。平面形状包括长度和宽度。它们没有高度作为维度。一些基本的平面形状是圆形、三角形、正方形、矩形等。
圆圈
圆是在平面上表示的有界封闭的平面形状。圆是一个二维图形,由一组点创建,这些点与平面中的固定点(也称为中心)有固定距离(也称为半径)。或者可以说一个圆由一个面组成,没有边或顶点。圆周上的点数是不可数的,线的方向随着每个点而不断变化。以下是圆圈中的一些常用术语:
- 周长:称为圆的边界。
- 半径:从圆边界上的任何点到圆心的距离。
- 直径:它是连接圆边界上存在的两个点的直线,它始终通过圆心。
- 弦:是与圆边界上任意两点相接的线段。
- 切线:它是一条与圆的圆周在一个唯一点相接触的线。
- 圆弧:圆的圆周的一部分,有小圆弧和大圆弧两种。
- 段:称为弦和圆弧所围成的面积。
- 扇形:称为由两个半径和圆弧围成的区域。
- 割线:它是在两个不同点处划分圆的线。
特性
- 如果两个圆的半径相同,则称为全等。
- 圆的弦与圆心的距离总是相等的。
- 当一个弦有一个垂直平分线时,该平分线从圆的中心经过。
- 当两个圆恰好在一点上相互接触时,它们被称为切圆。
- 圆的直径也称为圆的最长弦。
圆是平面形状吗
解决方案:
A circle is a plane shape as it is a closed figure. It is a figure that is represented on a plane surface. It is a plane figure formed by a single bounded curved line. The points in a circle are placed such that each point lies at an equal distance from the center of the circle.Therefore, each point of the circle is equidistant from the center and it is a two-dimensional structure. It can be stated that a circle is a plane shape.
示例问题
问题1:圆的直径是多少?
解决方案:
A diameter is a chord or line segment passing through the center of the circle. Diameter is considered to be the longest chord of the circle which passes through the center. Its length equals double the radius of the circle.
Mathematically, the formula for the length of diameter can be written as
d = 2r
问题2:圆的半径是多少?
解决方案:
The distance measured from the center to the circumference of the circle is defined as radius. It is the distance half of the diameter of the circle.
问题3:什么是圆的和弦?
解决方案:
In a circle, a chord is a line segment whose endpoints present on the circular arc or boundary of the circle. It Joins two endpoints in a curve. A chord can be measured in length as it has two fixed endpoints.
问题4:如何确定和弦的长度?
解决方案:
The length of a chord can be determined by the given mathematical formulas
- The length of the chord using perpendicular distance from the center = 2 × √(r2 − d2)
- The length of the chord using trigonometry = 2 × r × sin(c/2)