Curve, the path of a constantly moving point is an abstract concept in mathematics. Usually, such a route is produced by a balance. The word can also be applied to a line or to a number of line segments connected end to end. A closed curve is a route that repeats, enclosing one or more areas. Ellipses, circles, and polygons are simple examples. Open curves like hyperbola, parabolic, and spirals have endless lengths.
Shape of curve
The ellipses, circles, and hyperbola are two-dimensional curved forms, together with the arcs, sectors, and segments. In contrast, the three-dimensional curved forms, such as cylinder, sphere, and cones, are referred to.
Types of curves
In the different categories, curves are classified. Here are some examples of types of curves
- Simple Curve: A curve that alters its way, but does not intersect. The curve of this type is called a simple curve. There may be an open or closed simple curve.
- Non-simple curve: A non-simple curve is one that has more than one route. It indicates that the curve intersects itself when it changes direction.
- Open curve: A curve with two ends is known as an open curve because it does not contain the region within itself.
- Closed curve: When a curve has no endpoints and encloses a region or area, it is referred to as a closed curve. The open curve’s two ends are joined to produce this sort of curve.
- Upward Curve: An upward curve is a curve that points in the direction of upward movement. Concave upward or convex descending curves are terms used to describe upward curves.
- Downward Curve: The term “downward curve” refers to a curve that is pointing downward. Concave downward or convex upward curves are terms used to describe downward curves.
Example of simple closed curves
Triangle: A triangle is a form of a polygon with three sides, and the vertex of the triangle is where the two sides meet end to end. Between two sides, an angle is produced. One of the most significant aspects of geometry is this. The Pythagoras theorem and trigonometry, for example, are both based on triangle characteristics. The angles and sides of a triangle determine its kind.
A triangle is a two-dimensional closed form. It’s a three-dimensional polygon. Straight lines run along all four sides. The vertex is the intersection of two straight lines. As a result, there are three vertices in the triangle. Each vertex creates a unique angle.
In mathematics, each form has specific characteristics that set it apart from the others. Let’s look at a few of the characteristics of triangles.
- Three sides and three angles make up a triangle.
- A triangle’s angles must always add up to 180 degrees.
- A triangle’s outer angles always sum up to 360 degrees.
- A supplemental angle is the sum of successive inner and exterior angles.
- Any two sides of a triangle have a length that is larger than the length of the third side. Similarly, the length difference between any two triangle sides is smaller than the length of the third side.
Circle: A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a fixed distance from a given point, the center. The radius is the distance between any point on the circle and the center. A circle, in particular, is a closed curve that splits the plane into two regions: inner and exterior. In daily usage, the phrase “circle” can refer to either the figure’s boundary or the entire figure, including its inside; in precise technical terms, the circle is simply the boundary, and the entire figure is referred to as a disc.
Using the calculus of variations, a circle may also be described as a specific type of ellipse in which the two foci are coincident and the eccentricity is 0, or as the two-dimensional form encompassing the largest area per unit perimeter squared.
Square: The square is a regular quadrilateral with all four sides equal in length and all four angles equal. The square’s angles are right angles or equal to 90 degrees. In addition, the square’s diagonals are equal and bisect each other at 90 degrees.
A rectangle with two opposite sides of equal length is also known as a square. A square is a four-sided polygon with all four sides equal in length and all angles measuring 90 degrees. The square’s form is such that if a plane is sliced through it from the center, both parts are symmetrical. Each half of the square resembles a rectangle with equal sides on both sides.
Learn more from Basic Geometrical Ideas
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