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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

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

What are some good science fair project ideas for high school kids?

Do something about erosion.... it woks really well with an earth science fair project... also anything in math will extreamly wow the judges such as the number of __ in a bag of _____ or, the amount of ___ in and ______ area. i hope this helped!

How do you draw an isometric train?

I do not know!!!!:(

If you are drawing an isometric drawing by hand (pencil / paper), go purchase a 30 / 60 / 90 triangle (don't forget to use a straight edge to align the triangle).

If you are using CAD, change your snap to Isometirc and use CTRL + E to rotate between the planes (top, left, right).

Also use crating to help you draw curves!!

Who invented the isometric drawing?

First formalized by Professor William Farish (1759-1837), the concept of an isometric had existed in a rough empirical form for centuries.

What is the application of metric spaces in your practical life?

WOW! A LOT OF BIG WORDS! have a pretty wide vocabulary, but this is like college stuff! GOOD LUCK

What is azimuth degrees?

An azimuth is defined as a horizontal angle measured clockwise from a north base line. This north base line could be true north, magnetic north, or grid north. The azimuth is the most common military method to express direction. When using an azimuth, the point from which the azimuth originates is the center of an imaginary circle . This circle is divided into 360 degrees or 6400 mils . NORTH IS 0/360 AZIMUTH EAST IS 90. SOUTH IS 180. WEST IS 270.