Mathematics

Turns out that the sum of squares of the three distances, a2 + b2 + c2, is the same for all points on the circle. It appears as an algebraic "accident." What could be a geometric reason for this fact?

What is the term used for a radial that starts at a single point at the north most pole of a sphere and continues to equally expand and move to the alternate pole of the sphere until it contracts to a single point again please ?

Why do folks not get that logic and illogic are the literal two binding principles of our universe? Our universe was FOUNDED on logic an illogic. Big bang "A". What happened after in the physical we could say "B". What happened in the quantum we could say "the rest of alphabet all at once" Point is, it is all those two principles after the bang. It doesn't matter how you want to use math to explain it. There was an "A" and a "B". Logic and illogic are the only two things in existence that are part of the actual bang, itself. Because the bang is "A". Math didnt come until after Math is not real. It is an art form created to explain something

Hello everyone! I’m an assistant of a mathematical scientific researcher, and my research programme evolves around finding and developing all the (possible) solutions regarding all unsolved mathematical, logic, exact, and IQ puzzles ever created. If you search on the internet for: “The hardest unsolved logic math/iq puzzle/problem ever possible”. You would find the well-known "The Hardest Logic Puzzle Ever" (https://en.wikipedia.org/wiki/The_Hardest_Logic_Puzzle_Ever). I would like to gather some of your thoughts around this puzzle. The proposed solution on Wikipedia assumes that one of the gods must answer a factual question truthfully, leading to the conclusion …

1/2, 2/3, 11/15, 163/210, 619/770, 29/35, …? It’s the sum of reciprocal primes minus multiples’ overlaps plus subtracted multiples’ overlaps toward unity.

Hello I got the following proof, how do I begin to debunk it? Integer factorisation can't be polynomial for worst case scenario's. To prove this theorem, we use the fundamental theorem of arithmetic, which states that every integer greater than 1 can be expressed uniquely as a product of primes. We prove this by contradiction. Assume that there exists an integer n that can be expressed in two different ways as a product of primes, say n = p1 * p2 * ... * pm = q1 * q2 * ... * qn, where the pi and qi are primes and m ≠ n. Without loss of generality, assume that p1 is not equal to any of the qi. Then p1 must divide n, and hence p1 must divide the product q1 * …

1) The most basic works: + - X / counting, 1, 2,3 4...10, 100, 1000...... units, such as inch, feet, meter, hours, day, month. So we have to say people in Middle East and India did most of it. 2) I do not think Chinese did any, because Chinese "invented" writing very late. -Middle Easterners invented writing 5000 years ago. -Europeans invented a full set of writing symbols 7000 years ago -- Vinča Script. Vinča symbols, Wikipedia -Chinese invented writing 3500 years ago. Oracle bone, Wikipedia Chinese copied another's writing symbols. .

X, being a set, and Y being a set. X XNOR Y -> X XOR Y, is the basis of mathematics. Mathematics, based on my research, is about relationships which can be described using functions. These functions relate or create new sets. However there is a problem. What actually IS a relationship. Claim: A relationship is a symmetric difference -> symmetric addition. Explanation: A symmetric addition is a similarity between two sets. It is a comparison between these two sets and everything else in the universal set. By comparing both obtain something neat. Potentially a fractal. This is as far as I have gotten on the problem.

Good morning, I was thinking about this on a dog walk yesterday ( it makes the passage of time fly by) . How would I describe to someone for instance what the number 4 is without using other numbers or by applying something like addition or subtraction etc. Obviously you cannot say it is the number between 3 and 5 as that uses other numbers to define it. Then I thought about drawing 4 lines. But then of course I am mentally counting them as a draw them, and know when to stop in the addition. Next I thought of dice with their 1 to 6 in different patterns. 4 could be always that pattern of the 4 dots, which would negate any counting in the "descriptio…

Are there numbers that are to large for us to represent? Finite numbers... If we calculate the number of events/interactions that take place within a defined spacetime volume is it possible to represent that in a conventional way ,like 10 to power of some finite number? Eg a ball of lead with a mass of 1 kilo. Then ,if we extrapolate and our test volume is increased to include the observed or theorized universe ** that number defies imagination but is there any way to represent it? Not infinity because it is not ,I think infinite. Not measurable,quite obviously but what happens to our number system if we try to give it a number? …

Is the only reason that our mathematics are 10 based because we he 10 fingers and the first calculator was only our fingers ?

Hi team, I studies statistics in my first year of Chemistry study. That was many years ago but I found it to be an amazing topic. I would like to learn more about statistics. Presumably what people would learn if they did a second or third year course in statistics but I don't know where to find study material. What kind of textbook would teach me slightly more advanced statistics. I already know the basics of descriptive statistics as well as T tests, Z tests, Chi squad, regression, and ANOVA. As an example, I would like to learn how to do a meta-analysis. I got a book on Biostatistics and it seems to have a little bit of new content like geometric an…

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....

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…

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 …