Mathematics

Water Displacement Method This web-page says to use water displacement method to do so: https://sciencing.com/do-volume-object-6199021.html Another Way? But, is there a way to measure an irregular object without having to use the water displacement method for practical use with everyday objects? Gap Value The interesting thing about the formula for square or rectangled volume is that if used to measure irregular shaped objects, it would already contain gap information or gap values. The next step would be to find out how many amount gap number is then use total volume to subtract it to obtain an accurate volume for irregular object being …

To me, axiom-systems seem to basically be ownships (properties). For instance, the group-axiom-system is basically the ownship of being an ordered pair \((G, *)\) such that \(G\) is a set and \(*\) is a function from \(G\times G\) to \(G\) such that \(*\) is associative and has an identity element and each member of \(G\) has an inverse element with regard to \(*\). Just as the axiom-system itself is an ownship, so are what are called “propositions in the language/speech of the system” actually properties. For instance, when we say: “The proposition that the sum of the inner angles of a triangle is always 180° follows from the Euclidean axioms“, we actually mean tha…

I want to refresh some basic mathematics and i have difficulty getting some good notes on signed numbers Can anyone suggest me some good books to learn basic mathematics especially about signed numbers . Thanks

How do we solve polynomial equations? I only know how to simplify them. If you could solve this polynomial say N = 85 it would earn a million dollars. Remember who gave it to you. x^3 = N^2 * (x^2/(N^2/x + x)) Solve for x

Are there any good applications of research regarding spam/fake review detection?

I read that learning to use an abacus can help with one's own mental arithmetic... anyone experienced this? And any suggestions of a good abacus (type) to buy? Thanks in advance..

Do points lie on tangents lines "only?" From: "The slope of the tangent" Or on the curve itself?? If it's not on the curve, then: Where did that curve come from?? I'm not getting the ideas behind the following. ( x + delta h) I'm very familiar with linear equations but this does not clarify tangent points and the "fancy" albegra doesn't explain the evolution of time either cuz it sets everything at 0... Are these Points Hyper Planes?? Light Cones?? Faster Than Light Speeds?? N Gons?? Oragami?? ----->Standing Waves Maybe???

Is this as 2 pennies plus 6 pennies is 8 pennies?? could we also say 6/2 = 3 pennies Does this mean that all 3 pennies are1/2 * 6 pennies = smaller pennies? Im totally confused..

One thing I notice is that many shapes in 2-space; squares, circles, etc... can all have the common word "surface" apply to them. Even non-2-space descriptions like "the Earth's surface" still refer to the kinds of things that could intersect with each other at a point, along a line, along a curve, etc... just like 2-D shapes can. It seems the word surface more generally refers to that which is either 2-dimensional or could theoretically be unfurled to FORM something 2-dimensional. (Granted, if you did that with the Earth's surface a lot of people would get hypothermia pretty quickly!) Alternatively, it seems to refer to anything which Stokes' Theorem may apply to. Are th…

If x^2 = x/x = 1, why does 1 depend on 2 input values??? I get this idea from y' = 2x What if an input value was 3, does that make x cubed?????? y' =x^3 I'm totally confused..

Did Issac Newton know about numeral systems? IE Bases 10, 2, 1 etc etc? If not then, why do we use them "in calculus today??" Moreover, how can computers compute calculus? Issac Newton didn't have one, or did he?? Was it a Macintosh?? seriously.. This should be a very interesting thread..

As conciseness is one of main mathematical features, I would like to discuss one particular instance of it. Can someone please summarize in that context the usefulness of excluding number one from the set of prime numbers? As the definition of prime numbers would be more concise without it, ie if one was included, and in fact it was at the beginning, first great contributors to number theory who laid foundations to prime number theory considered it to be prime, exclusion was introduced later, without much change in the essence of the theory, so it must have payed off somehow in terms of development of shorter expressions of consequences of somewhat longer definition, and …

Is there a mathematical way to represent the formula itself? i.e. this sentence is about itself being informative

Whenever I write a sum in Latex, the limits appear forward of the sum sign. I have seen many instances where the limits are below and above. What is the code to get them there?

To start off: when we use 2pi*r = circumference.. Is 2 a coefficient? Or is it a natural number?

I had previously thought that this topic would suit in physics but decided in maths, however if not, I apologise in advance. Question: can we describe the unit of x in sine function in centimeter? for instance sin(x) is equal to 1 cm, where x is equal to π/2 centimeter. Some external comments: This question was a part of one of projects. Unfortunately I am not good in physics in the current position although I am willing to learn it but I saw (almost) no problem regarding its mathematical side. (because in fact as we know that sine function's domain set was R and value set was [-1,1] Maybe I am again failing because here the val…

What does it mean to have consecutive values in set theory? How are they related

e.g. defining them by specific (but no more than) several criteria. for instance can we say that if we have several specific points and that implied function is passing over these points, then that would be just one specific function. Or are there such specified functions? Thanks

e.g.: [math] \pi = \frac{22}{7} [/math] (only 4 operation is allowed)

The Russell set formula is inconsistent. But almost every language allows for contradictory or incorrect but grammatically correct formulas. For example, the arithmetic expression 1 + 1 = 5 is incorrect and inconsistent. Thus, Russell proved not the inconsistency of set theory (Cantor's), but only that the language allows for incorrect expressions

hi, I do not remember whether any function given in this category has had discontinuoum point. But with one notation: [math] -\infty, \infty [/math] are accepted as points. (This is real analysis) thus if any point accepts its limit one of these points,then this is not a problem. (however, one point cannot accept both of these points as limit point ,because this will be accepted as discontinuoum) elementary functions : LAPTE L: logaritmic A: arc P: polynomic T: trygnometric E: exponential. thanks.

So recently I was watching a movie (I'll not specify which in the interest of avoiding spoilers) where a character claims she'll curse another character's name until the day she dies, and then the character dies that same day. I know it sounds pedantic as all hell, but it got me wondering whether what she said was technically true. For the word "until" to be applicable in a discrete context, would more than one day have to be involved, or would one-day intervals also count? More generally, would "until" have to include the end date in the interval? I'm going to leave this thread open to other words as well, in case others are wondering about how other words' m…

I am trying to analyze graphs. but the interesting thing is that although I change the intervals sensitively, it gives me the same graph. (embodiment: try to draw [math] f(x)= x^{3} [/math] ,select first the interval [-2,2] and [-5,5] or symmetric else differently, see what happens.) so, can we...?

how to find the complexity of a formulation ( in terms of constraints and variables) (we refer generally to the notation (o(n^2) variables and o(n^3) constraints) ( i would be grateful if you mention links or examples explaining this question) - how can we justify a large gap in execution time for two formulations of the same complexity ?

What is the largest number value in base-10 you can write with just 3 digits? No symbols and characters allowed. Hints: it's not 999 Ask someone to write the largest 3-digit number and they'll respond with 999. Logical answer, but we can go bigger. Some may get the "power" brainwave and think of 999 (99 to the power of 9), which calculates out as 99×99×99×99×99×99×99× 99×99. Even better is 999 (9 to the power of 99) which calculates out as 9×9×9×9×9×9×9 ... and so on 99 times. The correct answer, however, if you extend the idea even further ends up as... 99^9 (9 to the 9th power of 9). Work out the second and third powers first (9×9×9×9×9×9×9×9×9 = …