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Topology

While geometry is primarily concerned with the mathematical properties of spatial objects, topology is concerned with the mathematical properties of those objects under continuous deformations. Please post all questions about topological subjects like homeomorphisms, manifolds, convergence, and connectedness, as well as their broad applications in computing, physics, and graph theory, into this category.

1,087 Questions

What is topology and example?

Topology is the study of objects (often surfaces in 3D) where details like position, shape and curvature are unimportant. Two topological objects are considered equivalent if they can be stretched to look like one another. An example of two different topological objects are a sphere and a doughnut shape (torus); the sphere cannot be stretched to look like the torus because it doesn't have a hole and the torus does.

How is an isometric scale constructed?

To make an isometric scale, use this table: Step 1 Action Along a horizontal line, mark off equal increments with any standard scale (figure 6-15, view A). 2 Using a 45° triangle, lay off lines from each of the increments. 3 Using a 45° and a 30°/60° triangles, form a 75° angle with the horizontal and lay off a line intersecting the diagonal lines. 4 Align a piece of paper, acetate, or cardboard, with the 75° line indicating equal increments. These increments form the isometric scale.

What is Isometric analysis in plumbing?

Isometric analysis is dealing with measurements in plumbing involving various items such as pipe fitting (using fittings and calculating the take offs or calculations for the various ones such as 90's, 45's, Tees, Tee Wyes, etc.) as well as grade or the slope at which gravity sewer is ran. Its basically a fancy term for the geometry, algebra, or trig formulas (overall mathematics used in the plumbing trade. Or at least that is what I have gathered. I am currently studying for the test in MS right now and I have researched this question myself.

How do you draw a circle in isometric projection?

Here is the link that will help you with Illustrations

http://www.ider.herts.ac.uk/school/courseware/graphics/drawing_circles_in_isometric.html

Does an isometric drawing use a vanishing point to create depth?

No. Isometrics are created using equal angles. Isometric drawings were made on "iso paper" but it is really just 45 degree lines on a page.

What shape is created by a cross section of a rectangular pyramid?

It is a rectangle which is similar to (but smaller than) the rectangular base.

What is the difference between Orthographic Drawing and Isometric Drawing?

orthographics means line is perpendicular to the view plane,while oblique means line is not exactly perpendicular to the view plane.

How do you draw an isometric letter a?

Like this? <a href="http://tinypic.com" target="_blank"><img src="http://i39.tinypic.com/2hyz0ug.png" border="0" alt="Image and video hosting by TinyPic"></a>

How is fault-tolerant different from redundant?

Although fault tolerance and redundancy both improve overall system reliability, the latter accomplishes that by adding circuit components. Ironically, adding components reduces MTBF (mean time between failures), since the more components a circuit contains the greater the failure rate must be. Think of this way: A power boat with two outboard engines will necessarily have a greater failure rate than a boat with just one engine, because it is twice as likely that an engine will fail. But ask any skipper whether he feels less comfortable about have two engines! Clearly, if a motor fails, you don't have to call Sea-Tow. Fault tolerance is different and a bit harder to define. Circuits can be overspeced and designed to within certain tolerances and accuracies. In a strict sense, when components drift out of those tolerances, the circuit is not performing to spec. You could say that a fault has occurred. But what if the overall system still performs its intended function with no apparent degradation to the end-user? We say those systems are fault tolerant.

What is a rectangle whose four sides are of equal length?

When all sides are equal it has a to be SQUARE. Which is the only shape that is a regular quadrilateral.

What is a digital line detector for a computer?

The jack for an analog phone line (the "regular" kind, where you could plug in a $10 phone and hear a dial tone) looks EXACTLY the same as the jack for a digital phone line, such as would be used in a business. They LOOK identical, but the line voltage and the signaling are completely different. Phones, modems, etc. that are designed to work with analog lines will not work, and can be damaged, if they're plugged into digital lines.

Digital Line Detect (DLG.EXE) is a program that's included with the modem driver software in most Windows notebooks (and some other computers.) It runs in the background, making sure you don't plug your modem into a digital line. If you do, it shuts down the modem to prevent damage and pops up a warning message.

If you're sure you won't be making that mistake, you can prevent Digital Line Detect from starting every time Windows boots up. It won't hurt anything.

Also - DLG.EXE is sometimes flagged as spyware, because the company that produces it also produced some spyware in the past. DLG.EXE itself is safe - but, as I said, you don't need it if you don't plug your modem into unfamiliar jacks.

How do you break down a one degree angle in trigonometry?

Into minutes, then seconds.

A 1 degree angle is 60", 0'

or, a 1 degree angle can be expressed as 0", 3600'

a .5 degree angle can be expressed as 30", and so on.

What is an isometric?

A form of three-dimensional projection in which all of the principal planes are drawn parallel to corresponding established axes and at true dimensions; horizontals usually are drawn at 30° from the normal horizontal axes; verticals remain parallel to the normal vertical axis.

How do you make a isometric drawing on isometric dot paper?

you can not draw horrizontal lines or it is automaticly wrong lol

What is water isometrics?

exhibiting equality in dimensions or measurements of water

What are the properties of a tetrahedron?

A tetrahedron is the smallest possible polyhedron: a closed 3-d shape with polygonal faces. It has 4 triangular faces, 4 vertices and 6 edges. It is also known as a triangle-based pyramid. Any other properties will generally depend on the particular tetrahedron.

How do circles appear in isometric drawings?

Circles appear in isometric drawings as an elipse.

In isometric projection how to draw pentagon?

Firstly Draw a pentagon and enclose it in a square. Then draw an isometric scale. With isometric reading draw the square first on 120degree axis, reduce the pentagon sides on isometric scale and plot it on the isometric square