Science Forums » Mathematics
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1w ago
I have a paper that, IMHO, proves the Collatz conjecture.  I will be looking at where to get it confirmed.  I welcome comments. Abstract:  The Collatz tree can be formed naturally, resulting in a good looking tree, but the numbers seem chaotic.  By reforming the tree, the tree becomes weird, but the numbers look nice.  And it becomes clear that the hailstone algorithm and its inverse can be used to traverse down and up the tree, from the root to all integers and beyond, and back to the root (the number 1). The link is http://dbarc.net/yr2024/collatz1.0.pdf ..read more
Science Forums » Mathematics
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1M ago
I have watched a video about the p-adic numbers:     Then, there is the Ramanujan's summation which is used in quantum mechanics (Casimir effect):   1+2+3+4+5+6...=-1/12 https://en.wikiversity.org/wiki/Quantum_mechanics/Casimir_effect_in_one_dimension This forum does not support Latex maths? Then, we have one more such summation: 1+x+x*x+x*x*x+x*x*x*x+x*x*x*x*x...=-1/(1-x) This is simple for x<1 and for x>1 we get:   1+2+4+8+16+32+64...=-1 1+10+100+1000+10000...=-1/9 1+20+400+8000+160000...=-1/19   Can we obtain all these sums with the p-adic numbers ..read more
Science Forums » Mathematics
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2M ago
So the expectation for this part of the lottery is $\frac1T\left(1 + \frac 1B(69-2B)\right)\cdot \1000000 = \1000000\cdot\dfrac{69 - B}{BT}$   1. Disregarding the messier LHS, how can I intuit the simpler RHS?   I know $\color{green}{\dfrac{1E6}{T} = \Pr(}$ winning $1E6 in the Gold Ball Draw). 2. But why multiply this $\color{green}{\dfrac{1E6}T}$ by $\color{red}{\dfrac{69 - B}B}$? 3. What does $\color{red}{\dfrac{69 - B}{B}}$ mean ..read more Science Forums » Mathematics by 2M ago Quote Since 30−B balls have already been drawn, this jackpot is$(69−2B)million.   As per the link overhead, the jackpot increases by $2E6 for every ball removed, I know. But where did this(69−2B) stem from? I feel like the author, Paul Sinclair, pulled it out of a hat! The maximum Gold Ball Draw jackpot is$68E6, not \$69E6. Then why did Paul Sinclair write 69?   ..read more
Science Forums » Mathematics
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3M ago
As far I can discern when inventing combinatorics I also found the product rule for differentiation and derivatives. Not "Isaac Newton" or some other name that I can't confirm ever existed. When pertaining to the scientific method, empirical evidence is based on observation which I don't rely on as heavily as mathematics for separating fact from fiction.  I know I don't get anything out of sharing an arithmetic that can literally be used to earn a person money for cracking a password combination or solving any type of Rubiks cube. I should be retired for this alone. I only share it becaus ..read more
Science Forums » Mathematics
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4M ago
what would it be then ..read more
Science Forums » Mathematics
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4M ago
What’s wrong with my reasoning in purple? Please pinpoint which sentence and step fails. I seek intuition. I DON’T want proofs, or formal arguments. Thanks! Presuppose lotteries let players pick any integer N≥32. Picking unpopular integers lowers your probability of winning lotteries. Why? Winning numbers range randomly from 1 to N. But you artificially narrow yourself to [32,N]. By disregarding [1,31], you flout the lottery’s random distribution of winning integers! As [1,N] contains more integers than [32,N], picking numbers ∈ [1,N] proffers more chances to win than picking ∈ [32,N]. Q.E.D ..read more
Science Forums » Mathematics
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5M ago
Hello all. Am on first steps to make a solar thermal water pump for drip irrigation purposes.    Assume 60% efficiency of solar thermal irradiation (600W/m2.     Assume average daylight temperature 25C.  Assume average night temperature 15C. Or, make those parameters real, entered in the formula.  Area of sun exposure as parameter, say =1 m2 (Tank lid)  Capacity of reservoir as parameter, say = 1 m3    Volume of air, =Va.  Volume of water =Vw. For a desired pumping height,  what would be the flow in 24 hours ? [Plus whatever ..read more
Science Forums » Mathematics
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6M ago
QuickBook Enterprise Help (+1-844-397-7462) Customer Care Number Quickbooks Support Number, Quickbooks Toll Free Number, Customer Service Monday through saturday from 8:00 AM to 9:00 PM ET and Saturday from 9:00 AM to 6:00 PM ET Number. Quickly Find The Quickbooks Customer  Number For All Your Tech Questions Benefits of Quickbooks When you use Quickbooks Online Support Phone Number   for your email needs, you get a number  of great benefits. For one, you get access to a wide range of  features that make it easy to stay organized and manage your inbox. You can also take adva ..read more
Science Forums » Mathematics
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7M ago
3x+1 if odd x/2 if even     So why not create a sieve of multiples of 2, 4, and 8?   When x equals a logarithm of 2, 4, or 8 then x/2 repeated equals 2.   2*2*2*2…   4*4*4*4…   8*8*8*8…   These 3 logarithms of 2, 4, and 8 encompass all the numbers that reduce to 2 when repeatedly divided by 2.   What am I missing? Did I break the rules of the pattern? I am trying real hard not to factor semiPrimes. I did not research the problem yet. I am only working with 3x+1.   I realize that this is more complex with larger numbers. I am just stating a simple ex ..read more

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