Daedalus
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Everything posted by Daedalus
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Hell yeah Md65536!!! You earned that rep. quick. I'm going to let this stand for a day or two before I post my usual break down to see if anyone posts the general solution for any [math]f(x)[/math] and [math]g(x)[/math]. Since we know you can do it, let's see if anyone else can figure that one out.
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My recent work on the Collatz conjecture has lead to the development of a method that allows me to merge the outputs of two functions into one function. To construct this new function, I only use the functions being joined, and elementary operations such as addition / subraction, multiplication / division, and exponents. Furthermore, I map the output of one function to odd numbers in the domain and the output of the other function to even numbers. So, the domain is restricted to integers, but the range can be whatever the functions output. This challenge is actually pretty easy, and the goal is to formulate the mathematics to join the outputs of [math]f(x)=2^x[/math] and [math]g(x)=3^x[/math] such that for the inputs / domain of { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... }, the new function produces the outputs / range of { 2, 3, 4, 9, 8, 27, 16, 81, 32, 243, ... }
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I have finally made a break through on the Collatz conjecture. Although I still cannot prove the conjecture, my work has allowed me to create two new challenges, one which will be the toughest one yet... I'll have them posted as soon as I can find the time to write them up.
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Ugh... I just got back from the ER and I officially have Influenza A
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Sounds like something my ex-wife would do...
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Nailed it!!!
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It has been one hell of a year! I've written lots of music, and finally found a great programming job! Next year is going to awesome!!!
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Check out this song my brother wrote for his daughter, my niece, Alizah Raymond. I had the honor of writing the orchestration for this song, which was easy considering my brother is one hell of a musician! Enjoy!!!
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Thanks Arc! I just wish I had better sounds to work with when rendering the songs. Now that I'm working as a Sr. Software Engineer again, it won't be much longer and I'll be able to upgrade my sounds, hardware, and all!!!
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Finally, the last composition of the year, and my new years resolution to write more music has been fulfilled as this is my seventh song this year. This piece is an orchestration of a song my brother and I play on guitar that we named "Forged by Destiny". Although this rendition isn't exactly how we play it on guitar, I'm sure you'll enjoy the song nonetheless!
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Yeah... I don't think I'll be buying a ticket any time soon. Virgin Galactic's SpaceShipTwo experienced "a serious anomaly", crashed in the desert, and killed one of the pilots with the other surely near death's door.
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After one week on the new job as the Sr. Software Engineer, I can truly say that I love my new job. The people are awesome, and the team really works together. I've already fixed a few bugs and have expanded one of our modules to include new functionality. The VP of Development is impressed with my work, and in his e-mail to welcome me to the team he mentions that I came in, hit the ground running, and already have fixes in the code for testing in our next release. High words of praise fo...
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Today is such an awesome day!!! I just got a new job as a software engineer for an awesome company, and I couldn't be happier!
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I'll look into it. Thank you Imatfaal.
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I'm definitely no sound engineer Imatfaal, and ProTools does have ways of modifying the dynamics. However, when I try to do the modifications, they just don't sound right lol. I want to get Vienna Instruments for ProTools. They have better controls for modifying dynamics. There are a ton of dynamics that I wish I could put into these songs. I'm going to try and get an appointment with a professor of music at OU or OCCC, and talk to them about what classes I could take and things I could do to improve those things. Until then, I do the best with what I have. Of course, if you or someone you know can help me polish these compositions into something more than what I have been able to record, then by all means speak up. As for now, the best way to listen to my music is with a headset. I mix everything in stereo, and it sounds much better through headsets.
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I just finished another composition. This one is called Variations in C Minor because I take the first theme and vary it through five different modes. Enjoy!!!
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Sure BODMAS could help you remember the order of operations, but why not let FEMA manage the emergency: Functions / Groupings Exponentials / Roots / Logarithms Multiplications / Divisions Additions / Subtractions
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I know what you mean Imatfaal. Right now I'm doing the best I can with the software I have. Unfortunately, when I add too many tracks or when the notes are too fast, then the software DSP can't keep up and it causes the audio to skip or adds artifacts in the music. What I really need is Pro Tools HDX + HD Omni so that I can add more tracks / voices to my music without having to worry about processing power. However, $10k is a little out of my reach. Perhaps one day, I'll be able to afford the equipment I need but, for now, I'll make do with what I have. I'm glad you enjoyed the music. I just wish I could do more.
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I know it's been a while since I've posted one of my songs, but I've been busy. This song is titled, "The Celestial Masquerade", and was inspired by a good friend of mine. Enjoy!!!
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Finding the Area Under a Circle Using Integrals?
Daedalus replied to metacogitans's topic in Analysis and Calculus
I see... My bad. I thought you were providing the answer for the region being integrated. -
Finding the Area Under a Circle Using Integrals?
Daedalus replied to metacogitans's topic in Analysis and Calculus
Studiot, I think you messed up on the calculation because [math]4-\pi = 0.858407346410206... \ne 0.31171910038781636...[/math] . -
Finding the Area Under a Circle Using Integrals?
Daedalus replied to metacogitans's topic in Analysis and Calculus
Using the integral, shifting the function as I did, and assuming a radius of 2, we end up with an interval [0, 1.5]. It is important to note that, even though the OP is integrating the left side of the circle, the symmetry of the function allows us to integrate either side as long as we adjust the limits of integration. Substituting these numbers into the integral yields: [latex]\int_{0}^{1.5}2-\sqrt{2^2-x^2}\, dx = 0.31171910038781636...[/latex] Of course, the antiderivative gives the same result: [latex](2)x - \frac{1}{2}\, x\, \sqrt{(2)^2 - x^2} + \frac{1}{2}\, (2)^2\, \text{tan}^{-1}\left (\frac{x \sqrt{(2)^2 - x^2}}{x^2-(2)^2}\right ) \Bigg|_{0}^{1.5} = 0.31171910038781636...[/latex] (For those not familiar with trig functions, [latex]\text{tan}^{-1} \theta = \text{arctan}\, \theta[/latex]) So, the answer you got Tar is a good approximation.
