Mathematics

Human beings that I have grown up around like to round numbers up, and fixate on one hundred, or a million, and more more commonly a billion in financial terms. I've never heard anybody say that they want to be a £950,000 thousand-aire, but a millionaire perhaps, yes. However, this is likely because we in the West use a base-10 system. But what of other base systems.. e.g. the "Yuki" language of California (USA) count the webbing between the digits on their hands and thus use base-8 (octal) system. In such a system, what would be the equivalent of "I would like to be a millionaire" ?

So I read that the geometric mean is a good indicator of central tendency when data is in logarithmic form. But to me, it would seem that this is a contradiction. Doesn't logarithmic data inherently not have central tendency? I should clarify that my understanding of "logarithmic" is that it means that changes are exponential. So if I have a data set of 1, 10, and 100, how could a geometric mean give me any useful data about the central tendency of this data set? There does not seem to be a central tendency....

I loved David Acheson's "The Wonder Book of Geometry". Can you recommend other books like that?

Hi, everyone! I'm planning on restudying math from the beginning (K-12), via KhanAcademy, MathIsFun, and plenty of other resources. Now, what I'd like to ask is, as the title says, should I study material grade by grade or topic by topic? Additionally, is there a way to test myself to know from which grade/topic I should start, like doing some sort of "evaluation test" or something similar whether on KhanAcademy or some other website? I'm asking this primarily because I know that early math will be a breeze to go through, so instead of wasting time on that, I would like to know if there is a way to start from somewhere where I'm weak and ha…

Can anyone help me with this question, I'm unsure on where to start Tides vary so the high tide and low tide height of the water is different every day. At certain times of the year, such as a Spring tide, the water can be very deep and it may not be safe to cross the inlet. During one big tide, the water was 3.9 metres deep at high tide and 0.7 metres deep at low tide. The Department of Conservation (DOC) recommends that walkers only cross the inlet within one and a half hours before low tide and two hours after low tide. Find a safe time to cross the inlet during this big tide and discuss DOC’s recommendation in relation to your findings for both tidal situations.

Me and a friend solved this binary once before in the past, using some kind of backwards logic. It doesn't convert straight to ASCII as it is is not really ASCII characters or even binary. It appears to be. But only in sense of language. While translating to ASCII from binary you might find that the result is completely encoded. So it's a sort of puzzle, in that sense, and it contains a message. The one time it did get translated, it was Douglas Engelbart. That's what it meant. I'm trying to remember how it was done. I'm asking for help on this. I remember that the first step was to translate the 'binary' on this page, which ignores types, to Hex, but to…

I suspect a complex equation from a simple premise the Butterfly Affect as opposed to the Butterfly Effect to describe the process by which small but socially significant events spark large social responses.

Greetings. This is not simple for me to put into words; please ask what I may be missing to expose properly. For a northern hemisphere latitude chosen as 450 as an average for America, Asia and Europe locations with solar panels. If the solar panels are placed horizontal, as soon as the sun is above horizon, the panels are exposed to direct sun rays. At a very low angle but every day of the year and for more than 12 hours in summer but at a 'lossy' incident angle. There will be a 'bell' curve of exposure peaking at celestial noon, producing a photovoltaic generation of X KWyear. If the solar panels are tilted 450 for optimal exposure, at sunrise above…

The title says it all. What operations do you need to carry out before you can do any sort of mathematics ?

Simple interest, compound interest, which are not difficult for most people. It is simple because the principal amount is usually fixed in calculations. In reality, the amount will change over time (i.e. customers may deposit or withdraw money from their account at any time). How does a bank usually calculate interest for their customers when the principal amount changes over time? Is there any such formula?

Hi, everyone! I'm preparing myself for the next year's college entrance exam, and I hope that 10-11 months of intensive study regime will be enough time for me to pass it. I would like your opinion on it to see if such a thing is possible and if there is anything that needs to be changed about my study program. The entrance exam which is on July, 1st is only 10 math-based questions from a random selection of topics listed here: https://pastebin.com/8yKZ26XY Now, here's the thing. All those topics that were listed in the above PasteBin link are the topics that are officially recommended on the college's site that students need to study for the exam, and what I'm c…

I took up classes again, to get high-school, and I struggled somewhat with math, the teacher didn`t really teach anything about how it works, only how to do it, but, I sort of still struggled, and I also noticed that more rational people struggle with it also, it`s like math is only there to filter out the people who aren`t really in the same group as the rest of the society, so, I`m not saying it`s for just irrational people, but I started to think about it a little, math I mean, in the old days they just used it for building simple houses and used inches, so here`s my problem with it then, if you take a ruler and measure the lenght of something, no matter how small you …

This is going to sound ignorant. I apologize ahead of time. I have limited knowledge of “The Traveling Sales Man” problem. But maybe the problem is drafting. If circle were drawn with the radius of the distance between 2 points would the straight line distance between where the circles intersect be the shortest path? That is easy to say. But I don’t know how to test it. I also haven’t studied current attempts. Is this similar to others attempts?

Hi, everyone! I'm planning on teaching myself math all the way back from the basics, up to high school stuff. It has been a long time since I studied math. I've never been a great student back in school. I daydreamed most of the time, and when it came to math, I always rote learned and memorized things just enough to get a passing grade, sometimes I got lucky and managed to get a perfect score, but those moments were rare. Because of that rote learning, and memorization, I have forgot almost everything about math other than the basic arithmetic, and even there, it takes me a bit of time to calculate simple problems :( However, now, that I'm older, I fo…

Hi all, not sure if this is the right place ask for help with using Javascript to calculate a curve for Exponential Growth / Decay... I have a form element that has a Min, Max, and Rate, where if the Rate slider is set to 0, its just straight Linear Growth... Im trying to mirror functionality from these Window Forms: What I'd like to do is to move the Range (where it says Fast Middle Slow) so the output looks like this: This is my function so far... function calculateValues(){ if (level1.value == '' || !level1.checkValidity()) return; if (level99.value == '' || !level99.checkValidity()) return; let rate…

Hi everyone. I just got a game for the Nintendo Switch called Menseki Genius, which has Area Maze puzzles in it. I've been staring at the very first puzzle for quite a while, and I'm stumped. Attached is an image of it. My initial figuring was that since the rectangles with areas 11 and 13 are prime numbers, their lengths and widths have to be 11x1 and 13x1, respectively. Working from there, I figured out some other sides, like the other side of the 22cm rectangle being 2, etc. But this isn't making complete sense, because that would make one of the sides of the 20cm rectangle 12, which has to be wrong. I've tried looking up how to solve these puzzles, but …

Hello, I have been a A student for a few semesters at my local college but this semester is been kicking my butt. I wanted to ask some advice regarding my math classes and programming class since I seem to have a deep struggle which hasn't gotten to be quite serious. So the math classes I am taking are linear algebra, discrete math, and Calculus II. For programming its C++ part 2. The habits that I notice is that: 1) I don't get enough time to absorb the material to improve my knowledge when it comes to any given concept. 2) I usually can't understand my notes and it seems my Professor and classmates aren't able to help me out either I can't …

In GCS coordinate system the North Pole is +90, +0; Great Pyramid of Giza is +29.9, +31.1; and +0,+0 is in the Atlantic Ocean, South of Ghana. Assume The Great Pyramid of Giza +29.9 +31.1 is the new north pole +90,0, so new coordinates of other places will have to be- Aangkor Wat= +0,+90; Nazca lines= +0,-90; Machu Pichu= +8,-90 etc. What is the equation to find longitude and latitude of any place if The Great Pyramid of Giza is the new north pole of the earth? Note that it's not important to keep current north pole at +180 longitude. But if you know equation to keep it at +180 and calculate other coordinates that's good for me.

Never saw before. Several figures written different. -Image borrowed from the web-

One solution to global warming could be to view greenhouse gas emitting objects as an ecosystem. In that ecosystem would be vehichles, factories, etc. Once the ecosystem of greenhouse gas waste is identified, it would be possible to deduce how that ecosystem mates wth the human race. Vehicichles, a mathematical function of the human need to travel efficiently. Factories, the result of human desire to produce goods and services quick time. Efficiency, therefore is the key propellant of greenhouse gases. There is the need for efficiency over a broad range of human activities, therefore, there is greenhouse gases. True or false? So how to …

Can anyone explain in one paragraph or equation how the Riemann hypothesis implies a pattern in Prime numbers? The hypothesis an easy enough to follow the problem, but the pattern in Primes is not clear to me. I’m sure a Google search may be helpful, but I wanted to work it through on my own. I find it helpful to take one small part if the problem and see what it does. Take the book Practical Cryptography. It explains all the ciphers. They are all open source. Doesn’t mean you can solve them but it lets you see the inner workings. That is what I need an explanation of the patterns in Primes in the Riemann hypothesis. I hope you understand why I just don’t g…

When did the world begin? With the big bang, wasnt it? Just before the big bang, there was the big shrink (the previous universe condensing into a nano particle, like a micro-atom). All that is pure science. Well, what happened between point A (the big shrink finishing shrinking) and point B (the big bang about to happen) Which equates to absolute zero? So if Zero is a virtual number, then the universe is an illusion. But if zero is real, then so is infinity. Infinity is the polar opposite of zero. The polar opposite of real is also real.

Let us consider a transformation $T$, which converts a vector into a symmetric matrix, e.g. Xh=[x1,x2,x3]T , then \(T(X_h) =. I want to have this type of decomposition: T(QXh)=Q¯T(Xh)Q¯T. Here, $Q\in \mathbb{R}^{m\times \frac{q(q+1)}{2}}$, $\bar{Q}\in \mathbb{R}^{p \times q}$, $T(X_h)\in \mathbb{R}^{q \times q}$ and $X_h \in \mathbb{R}^{q(q+1)/2}$. For example: Consider a known constant matrix $Q \in \mathrm{R}^{10 \times 3}$. A vector $X_h = [x_{11}, x_{12}, x_{22}]^T \in \mathrm{R}^3$. Decomposition must be like, T(QXh)=Q¯T(Xh)Q¯T=Q¯[x11x12x12x22]Q¯T where, $T(QX_h)\in \mathrm{R}^{4 \times 4}$, $\bar{Q…

My tests are submitted and marked anonymously. I got a 2/5 on the following, but the grader wrote no feedback besides that more detail was required. What details could I have added? How could I perfect my proof?

I grok, am NOT asking about, the answers below. Rather, how can I calculate the final answer DIRECTLY, without division? I don't know why my Latex isn't rendering here? Please see https://math.codidact.com/posts/285679. Orange underline 1. Unquestionably, $\color{#FFA500}{4 \times 3/2} = 3!$ But how can I construe 3! DIRECTLY WITHOUT DIVISION? What does 3! mean? Here's my surmisal. Blitzstein's solution hints to this calculation, but he didn't write 3! explicitly. You fix the first person. Then of the 3 people left, you can pick the 2nd person in your 2-person committee in 3 ways. Is this correct? Red underline 2. Unquestionably, ${\color{red}{\d…