They are either above or below the plane in space. They can be viewed as Online Accounting either floating above the plane in space or below the plane in space.

A plane is usually represented as a closed four-sided figure and is named by placing a capital letter at one of the corners. Any plane section of an elliptic cone is a conic section. Depending on the context, a flat surface that extends infinitely and has no depth “cone” may also mean specifically a convex cone or a projective cone. A cone with a polygonal base is called a pyramid. A line line segment is part of a line having two points, called endpoints.

The Object With Finite Volume But Infinite Surface Area

Euclidean geometry, sometimes called parabolic geometry, is a geometry that follows a set of propositions that are based on Euclid’s five postulates. A segment is a diagonal of a polygon iff its endpoints are non-consecutive vertices of the polygon. A polygon for which one segment connecting non-consecutive vertices lies outside the polygon is a concave polygon. A polygon in which all segments connecting non-consecutive vertices lie within the polygon is a convex polygon. Adjacent angles are a linear pair of angles iff their unshared rays form a line.

a flat surface that extends infinitely and has no depth

A line segment does not have a set of CONTINUOUS points like a line does. Endpoint means that a line has a beginning and an end. The notation for a line segment in a bar over any letter of choice. Say AB has a bar over it, you would read it as “line segment AB.” A line is a set of points extends in two opposite directions without end. It is identified by naming two points on the line or by writing a lowercase letter of choice after the line. Mathematics can extend space beyond the three dimensions of length, width, and height.

A Flat Surface That Extends Infinitely And Has No Depth; It Has Length And Width

We then refer to “normal” space as 3-dimensional space. A 4-dimensional space consists of an infinite number of 3-dimensional spaces. The greatest ocean depths on the Earth are found in the Marianas Trench near the Philippines. Calculate the pressure due to the ocean at the bottom of this trench, given its a flat surface that extends infinitely and has no depth depth is 11.0 km and assuming the density of seawater is constant all the way down. where P is the pressure, his the height of the liquid, ρ is the density of the liquid, and gis the acceleration due to gravity. Then we take P to be 1.00 atm and ρ to be the density of the water that creates the pressure.

a flat surface that extends infinitely and has no depth

If we want to talk about two or more different planes, then we need to be able to name each plane. Most frequently, you use three or four of the points that are in the plane as the name. Remember that points are indicated with a dot and are labeled with a capital ledger account letter. The second way to name a plane is with just one capital letter that is written in the corner of the image of the plane. This letter does not have a dot next to it and is sometimes written in a script font that is different from the font used for points.


Calculating the Mass of a Reservoir from Its Volume, we calculated the mass of water in a large reservoir. We will now consider the pressure and force acting on the dam retaining water. (See Figure 2.) The dam is 500 m wide, and the water is 80.0 m deep at the dam. What is the average pressure on the dam due to the water? Calculate the force exerted against the dam and compare it with the weight of water in the dam (previously found to be 1.96 × 1013 N). Explain the variation of pressure with depth in a fluid.

  • As for a line segment, we specify a line with two endpoints.
  • Either half of a double cone on one side of the apex is called a nappe.
  • In the case of lines, the cone extends infinitely far in both directions from the apex, in which case it is sometimes called a double cone.
  • All possible lines that pass through the third point and any point in the line make up a plane.
  • A line exists in one dimension, and we specify a line with two points.

, which brings every triangulated surface to a standard form. ), the surface is not orientable , so there is no difference between attaching a torus and attaching a Klein bottle, which explains the relation. If f is a smooth function from R3 to R whose gradient is nowhere zero, then the locus of zeros of f does define a surface, known as an implicit surface. If the condition of non-vanishing gradient is dropped, then the zero locus may develop singularities. The image of a continuous, injective function from R2 to higher-dimensional Rn is said to be a parametric surface. Such an image is so-called because the x- and y- directions of the domain R2 are 2 variables that parametrize the image.

Lesson Summary

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a flat surface that extends infinitely and has no depth


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