Sometimes math problems appear to be incredibly simple. But what’s contracting?
Q: How is it that Bell’s Theorem proves that there are no “hidden variables” in quantum mechanics? Q: Are beautiful, elegant or simple equations more likely to be true? Proving godel's theorems and learning recursion theory was the most challenging thing I have ever learned in my entire life. A more general treatment can be done using Noether’s Theorem, which says that every symmetry produces a conserved quantity. Q: If you are talking to a distant alien, how would you tell them which way is left and which way is right? So, there are some of the brain discipline scholars who think that left brain thinkers generally have a tendency to appreciate things in chronological order while right-brainers are more worldwide as they collect a lot of information in one time only. Q: How does a gravitational sling shot actually speed things up? Q: Why do heavy objects bend space and what is it they are bending? Q: What determines the size of the bright spot when you focus sunlight with a lens? You can describe it simply and in such a way that anyone (with sufficient time and chalk) can find as many digits of π as they like. Why use approximations when the exact answer is known?
Q: When you write a fraction with a prime denominator in decimal form it repeats every p-1 digits. Q: Is the final step in evolution an ascension into an energy-based lifeform? Q: Why is the area of a circle equal to πR.
The primes below 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. Change ), You are commenting using your Google account. Q: Why is the integral/antiderivative the area under a function? So what’s the most (but not needlessly) complicated equation in the universe? Doing the same thing for x or y, you get , which says “things don’t accelerate sideways”.
Notice that this sum is just the function on the left hand side of Equation 2 (the Euler product formula) earlier in this post, with s = 2.
Sometimes for a student becomes very proficient and experienced in Maths. Q: How can carbon dating work on things that were never alive? Quadratics with a given sign for the quadratic Q: What is the universe expanding into? What is your favorite topic in math? 1.Goldbach Conjecture. How can they be sure that all life uses water? ( Log Out / Q: Who would win in a fight: Gödel or Feynman? The equation \(ax^2 + bx + c = 0\) can be rewritten (when \(a\) is not \(0\), after dividing by \(a\)) as, \[(x + \frac{b}{2a})^2 = \frac{b^2-4ac}{4a^2}\].
Your email address will not be published. Could black holes take you to other universes? I’ll give 2 trillion dollars to anyone who can solve 1/0(without breaking math or creating a nonsensical function). The quadratic or trinomial equation is NOT beautiful.
Differential calculus is about approximating more complicated functions by linear functions. Yet if you square all the numbers, it doesn’t add up to infinity (it adds up to pi squared over six). Q: How does the expansion of space affect the things that inhabit that space? Q: What are integral transforms and how do they work? The equation above is an explicit function for the number of primes less than or equal to a given number. What is it about matter that causes that to happen? Q: Is quantum randomness ever large enough to be noticed? Is the “brown note” possible? I am in third grade. My physics professor is always setting up problems for us, and then saying "the rest is just algebra, and if you cant do that, you should not be in this class" Which is true, no doubt, but I dont like the implication that it is "just algebra". What is the difference between batteries with the same voltage, but different shapes or sizes?
Are atoms, people, stars, and everything else getting bigger too?
Could you ask them which slit they went through afterwards? Q: If you could see through the Earth, how big would Australia look from the other side? Theoretically, which type of vision would be the best to see things with? Q: What makes natural logarithms natural? A surprising amount of mathematics is actually easy once you've learned it. The Analytic Continuation of the Factorial, The factorial function is commonly defined as n! By “we” I mean humans.
Relativity and Quantum Mechanics: the elevator pitch. quadratic functions; these have the form, \(ax^2 + bx + c\), where \(a, b\) and \(c\) are Q: How can quantum computers break encryption? Speaking from what little I have done, I found algebra hard, specifically just logrithms. Most all of the functions we will talk about can be formed by starting with three basic
If the Earth was flat and had infinite area, would that change the answer? And the Euler Product Formula is also great for its simplicity. One thing that you didn’t mention is the sheer simplicity of many of these, a factor which really contributes to their beauty.
How do we know that God really does play dice with the universe?
My calc III class started by stating the l-p norms and using them in proofs.
where (note that this number is the Golden Ratio). Q: Is there such a thing as half a derivative? The simplest polynomials are the linear functions we have already mentioned. Good luck. The “action”, , is a function of the path a system takes, . Q: Is there a real life example where two negatives make a positive?
The importance of learning in a subject like Mathematics cannot be explained because it is studied in different ways. Q: Does how you deal cards affect how random they are? Q: Why can’t you have an atom made entirely out of neutrons? Q: Are explosions more or less powerful in space? Q: What is the “monogamy of entanglement”? Is it actually feasibly possibly for some ‘being’ to have just existed, infinitely? The Gap between the subject matter and the learner: When the tough or difficult mathematics content is being taught to the students and they do not understand the subject taught to them and goes out of their mind, serious achievement gaps duly occur and this situation only occurs if the students are not regular or transfer to another school during the academic session. Amazingly enough, this formula will always give an exact integer! How are the atoms in living things any different from the atoms in dead things? functions, and applying the operations of addition, subtraction, multiplication, division, One teacher I had was introducing a new concept, and we did an example in class. Can any color of light be made? The concepts are basically built upon various topics and are generally related to previous learning throughout the session. Q: How do those “executive ball clicker” things work? Q: How does quantum physics affect electron configurations and spectral lines? and later astronomy; today, all sciences suggest problems examined by mathematicians, and many
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