Dear Serbian Smartypants, I'm sure he only meant high school math class was the last time he had to use these concepts, not that it's where he first learned them all. Arrogance isn't attractive.
In the first place, Eurocrum, I'm a she not a he, and in the second place I was a social worker and then a stay-at-home mom, neither of which had a lot of call for math vocabulary, especially since my kids were brilliant and didn't need help with their homework. And in my younger days in the 1950s and '60s, many of those terms weren't taught until high school if even then. Some of the terms on here we were never taught - factorial, natural numbers, summation. I am amazed now to look at the math homework of my younger grandchildren. They are doing math we never heard of until higher grades. I think that's a great thing and I wish I'd had the chance to learn more. But there's no need for you to be arrogant because you know more than I do on the subject.
I find most serbians are jerks. Relax serbians I am just making a callous generalization the way eurochem did. I only know one serb and he's pretty cool.
I really hope you realize that you all sound arrogant. It's these kind of comments that deter me from going on JetPunk. Most of it is just people saying their age and their time and bragging about it, people attacking others who said the wrong word and someone takes full offense for that, or some sexually biased crap that makes it look like users of JetPunk are sexually biased into thinking women aren't allowed to get 100% on a quiz. I'm not insulting Quizmaster and his policies, but I'm warning that even JetPunk can turn out like Facebook.
Yes, velocity is indeed a vector, but not every vector measures speed and direction. A vector could just as easily represent displacement (distance and direction) or acceleration and direction.
Agree with Scuadrado - a vector is a magnitude and a direction, which can represent a number of real-world (and theoretical) phenomena - acceleration and force are two real-world examples.
You could stop the circle-jerk of semantics and just take the quizzes. Obviously if you're that well informed, this quiz doesn't pose much of a challenge to you anyway.
points have no dimension, lines have one, and planes have two. Think of how many numbers it takes to specify your position if you were within the entity in question. You're either on the point or off it, so you don't need any number to tell you where you are; you can be on a line at point 4, or -36.845, or any spot specified by one number that tells you how far along you are; and the plane takes two numbers.
@GameKitty maybe what they were trying to say was that a line drawn on a board or on a piece of paper does in fact have some width (and technically some depth as well even though its just a layer of chalk or ink) which makes it kind of 2 dimensional. but the mathematical definition of a line is something that only has 1 dimension.
The square root of a negative number is in fact complex, but so is the square root of a positive number, so that would be a really vague answer (like accepting "that one country" on the Countries of the World Quiz)
There are multiple types of averages. There are the mode, median, arithmetic mean, geometric mean, harmonic mean, and possibly others I don't know about. None of them are THE average - they are all AN average.
There are a great many different types of mean. Quadratic mean is probably most common after the ones you listed - you square all the data, take the arithmetic mean of that and then take the square root. E.g. To find the quadratic mean of 1, 2 and 2, you square then all: 1, 4, 4. Take the arithmetic mean of that: 3. Then take the square root: √3.
In fact, given any smooth one-to-one function from the positive numbers to the positive numbers it is possible to construct a mean based on that function. The functions for different means are: Arithmetic Mean: f(x) = x; Geometric Mean: f(x) = log(x); Harmonic Mean: f(x) = 1/x; Quadratic Mean: f(x) = x^2.
To be pinickity, i is called THE imaginary number, and numbers of the form a + bi are complex numbers. So the answer "imaginary numbers", strictly speaking, is wrong. At least set it to accept complex numbers and I will be satisfied
Actually, it's not wrong. You're correct that numbers of the form "a+bi" are called "complex numbers", but square roots of negative numbers take the form "bi" and are all called "imaginary numbers". i is the "imaginary unit".
You should accept Platonic Solid for "...Tetrahedrons and Dodecahedrons...". I got so hung up on these being 2 of the 5 platonic solids that I figured I was spelling platonic wrong! Polyhedron is correct of course, this is just an alternative.
There is no such thing as the square root of negative numbers. The square root is a function defined from the positive numbers to the positive numbers. No analytic continuation to the negative number is regular. Imaginary numbers are numbers whose square is a negative number and no, it's not an equivalent definition.
As for those who say the answer should be "complex numbers", that's wrong. The square of any complex number is a complex number (for example : (1+2i)²= -3 + 4i ). It's only the pure imaginary numbers that give negative numbers.
Not all complex numbers are imaginary, thus "complex number" can't be accepted for this question (which should still be corrected, by the way, everytime I read that, my eyes bleed).
Technically I think Arp is correct. In the field of complex numbers for every complex number z there are actually two complex numbers a such that a^2 = z. In the case of -1 these numbers are i and -i. It is possible to define a function, however, that is defined from the complex numbers to the complex numbers that could reasonably be called a square root - and it is the solution x to the equation x^2 - z = 0 with either the greater real part of if both real parts are the same the greater imaginary part.
Perhaps reflects my advanced age, but we learned the positive integers as 'counting numbers'. Counting number in wikipedia redirects to natural numbers. COuld you add that in? And as mentioned above, please accept platonic solid - or make one of your examples an irregular polyhedron.
Stuff like "scalene" is useless vocabulary that you shouldn't need to know; you just need to know the actual math behind it. Whoever thought they had to create some fancy word just to define a triangle with sides of different lengths was out of their mind.
In the expression a/b=c; c is called the quotient; a is called the dividend, and b is called the divisor, a is also called the numerator and b is also called the denominator.
Quizmaster should accept divisor as well as denominator.
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.
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.
I live in Serbia, and we learned 90% of these in elementary school.
But isn't it sad that he didn't use that after high school? :'(
Kids have to learn more today, and if you ask me, they should learn even more :)
Physics is very similar to math, with a tad bit of science added in there, so I think it belongs there.
No they aren't. :)
Two, silly, an inside and an outside!
Quizmaster should accept divisor as well as denominator.
Read the first axiom in the section on formulation.
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.