Tetrahedrons and dodecahedrons are actually "regular polyhedrons," since they both have congruent edges and faces, and only a few other polyhedrons fall into that category. Please accept that answer as well.
I've heard it both ways. Natural numbers usually include 0 in theoretical computer science especially. In my experience people use the term "positive integers" when they want to exclude 0.
Sorry to repeat myself, but seriously, an imaginary number is a number whose square is a negative number, not the "square root of a negative number". That may seem to be equivalent, but it's not. Of course, you have to know a bit about functions to understand that...
Of course, it actually is equivalent. This is a commonly accepted fact that is taught everywhere. Every number has two roots, and every negative number has roots that are imaginary.
You can define a square root of k as a root of the equation x^2 - k = 0. Then imaginary numbers are square roots of negative numbers. A square root is not always a function.
I also don't like that definition of a prime number, because it doesn't clearly exclude the case of 1 ( 1 is NOT a prime number ). The correct, though less explicit definition, is simply to say that a prime number is a number with exactly two positive divisors...
It is extremely hard to make math fun, but there are some very interesting parts to it, but those are what mathematicians haven't discovered yet, sadly.
Was this a joke? Math and Maths are the same subject right?
In my life I've only used 8 of these facts for any worthwhile purpose. The rest have been stored away in my brain , since my schooldays, like an old book in a library that nobody reads .
I would like to add to the cause of counting numbers. It's been nearly 30 years but I distinctly remember those terms being synonymous and the world of google tends to agree.
I would consider adding "square" for two-dimensional line. I've spent some time learning about hypercubes, and the example everybody always uses is that a point is 0 dimensions, a line is 1, a square is 2, and a cube is 3. Going off of this example, the logical answer for "two dimensional line" would be a square. I eventually did get plane as the right answer, but I still think square should be added as a type-in.
To be pedantic, a "Three-dimensional version of a circle" is a 3-sphere (a 3-dimensional hypersphere). A normal sphere has only two dimensions: e.g. latitude and longitude. While spheres are often embedded in 3-dimensional space you can also embed a sphere in 4-dimensional space, so it's not really saying much.
A circle is defined as the set of all points in a plane that are a fixed distance from its centre. A sphere is the logical continuation replacing a plane with 3-dimensional space. You can embed a sphere in 4-dimensional space but it will no longer be the set of all points a fixed distance from the centre.
The original commenter is technically correct; an ordinary "sphere" is actually a 2-sphere, a 2-dimensional surface embedded in 3-dimensional space. A 3-sphere would actually be embedded in a 4-dimensional space. A more accurate answer would probably be "ball," which refers to not only the sphere but also the space enclosed by the sphere.
That is the case in topology. But the most natural definition for a circle in Euclidean geometry requires two dimensions, and a sphere would be the result in three dimensions. The circle itself, though, is I suppose one-dimensional. A ball would be the three-dimensional equivalent of a disc.
Hmm, hard when you're not native English. Got 16/20, but I was typing 'regular solids', 'faculty, facultation'. 'irreal numbers, complex numbers'. Never heard of Scalene.
Strictly speaking, the object commonly referred to as a sphere is only two-dimensional (while a circle has only one dimension). The answer "ball" should also be accepted; the space bounded by a 2-sphere constitutes a three-dimensional ball: https://en.wikipedia.org/wiki/Ball_(mathematics)
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 should be accepted as an answer to 10 to the 100th power
Please consider accepting "cylinder" for "three-dimensional representation of a circle." I understand why sphere is more widely answered, but I would argue that not only is a cylinder a three-dimensional representation of a circle, but that it is also a better answer to the question as it really only is a circle extruded over a third dimension rather than a circle rotated around an axis.
A circle is defined in 2-dimensional space as the set of all points that are a given distance from the circle's centre. If you replace 2-dimensional space by 3-dimensional space you get a sphere.
Add depth to the circle to get a cylinder. Add depth to a square and you don't always get a cube. It can be a rectanguloid. "3-D circle" is not good enough.
Imaginary numbers are a subset of the complex numbers. No complex numbers that are not also imaginary numbers are ever square roots of negative real numbers. So imaginary numbers are the correct answer.
Wow that was...humbling. 10/20. it's always been my weakest subject, but yikes. I have apparently forgotten most of the math I learned in high school and college lol.
can you change the polyhedron question to a definition as in the description at the top of the quiz? the question at the moment just gives two examples and ask for a category they belong to.
Read the first axiom in the section on formulation.
Any number like this i*x (x being real) will lead to :
(i*x)²=-x²
Any complex not real nor imaginary like x+i*y will give :
(x+i*y)²=x²-y²+2i*xy (the only solution to get a negative real number is x=0)
Was this a joke? Math and Maths are the same subject right?
1) A three dimensional version of a circle doesn't have to be a sphere. It could be a cylinder
2) I would argue that a "two-dimensional line" is a line.
-Keegan Michael Key
for 10^100 :(
The questions, the comments, that blissful thing about maths, everything is just perfect here!