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q-binomials – Bedtime mathematics
https://mymbl.wordpress.com/2011/09/17/q-binomials
Mathematics that is slept on…. What to expect in here. September 17, 2011. The binomial like coefficients that we saw in earlier posts:. 8211; binomial coefficients. In keeping with the existing convention we will use. As the indeterminate instead of. It was established in an earlier post that:. Using this identity we may reduce the. We also made use of the identity:. In the above equation, we get. We now discuss a few consequences of the above identities:. For any natural number. Is a prime,. You are co...
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svark – Bedtime mathematics
https://mymbl.wordpress.com/author/svark
Mathematics that is slept on…. What to expect in here. October 23, 2015. The strong convex hull property says that for a spline of degree , the convex hull of at most control points of a spline contains the point of a spline at parameter . Intersection methods can use this property to rule out certain interections. Union of a convex hulls of consecutive points completely encompass the… More sandwiching a spline. Tightly bounding a bspline. October 8, 2015. Tightly bounding a bspline. September 14, 2015.
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What to expect in here – Bedtime mathematics
https://mymbl.wordpress.com/what
Mathematics that is slept on…. What to expect in here. What to expect in here. Mostly expository posts on variety of topics math I study or a problem I slept on last night. Stuff I would like to clarify for myself and may be of independent interest to others as well. Leave a Reply Cancel reply. Enter your comment here. Fill in your details below or click an icon to log in:. Address never made public). You are commenting using your WordPress.com account. ( Log Out. Notify me of new comments via email.
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a result concerning cyclotomic polynomials – Bedtime mathematics
https://mymbl.wordpress.com/2011/04/24/a-result-concerning-cyclotomic-polymials
Mathematics that is slept on…. What to expect in here. A result concerning cyclotomic polynomials. April 24, 2011. August 15, 2011. In this post we record a useful result concerning cyclotomic polynomials. This will help us prove what is claimed in this post. For distinct positive integers. The GCD of the values of cyclotomic polynomials. On the other hand, if. We will start by proving that the gcd. Is a prime power. Let. And assume to the contrary that. The values of cyclotomic polynomials. Is a power of.
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arc length – Bedtime mathematics
https://mymbl.wordpress.com/2015/04/23/real-worldish
Mathematics that is slept on…. What to expect in here. April 23, 2015. April 17, 2016. In this post we look at an algorithm to compute arc lengths of a differentiable curve. First lets recall the definitions:. Be a the curve parametrized by. Try this in wolfram alpha for example:. Integrate[Sqrt[1 x 2 x 2 x 5], x]. This is a tractable problem and definitely can be evaluated for polynomial curves but it is way off the result. Lets us see the connection between the two. Since we have come this far, let tak...
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Waist on a torus – Bedtime mathematics
https://mymbl.wordpress.com/2011/11/22/waist-on-a-torus
Mathematics that is slept on…. What to expect in here. Waist on a torus. November 22, 2011. August 24, 2012. Last year I worked on a interesting problem which asks about the possibility of partitioning a convex set in a plane in to. Internally disjoint convex pieces of equal area and perimeter. The problem has since been proved when. There is a pair of separators of a torus along its “waist” that map to zero under. More specifically, there is a subset. Of the zero set of. Label the coordinates of. Be the...
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ponder problem now on last legs – Bedtime mathematics
https://mymbl.wordpress.com/2011/05/01/ponder-problem-now-on-last-legs
Mathematics that is slept on…. What to expect in here. Ponder problem now on last legs. May 1, 2011. May 1, 2011. This post culminates our efforts in solving the problem. Are positive integers with. And satisfying the following. For all positive integers. Is a power of. First recap a few facts from this post. We began by showing that:. And therefore by the lcm,. We however wanted a stronger divisibility condition that. Should be divisible by,. For then, the sequence,. Vanishes, showing that. On the probl...
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an old ponder problem – Bedtime mathematics
https://mymbl.wordpress.com/2011/04/22/an-old-ponder-problem
Mathematics that is slept on…. What to expect in here. An old ponder problem. April 22, 2011. September 17, 2011. It is well-known that if natural numbers. Is a multiple of. April 2005 ponder asks whether the converse is true, that is if for integers. Is a multiple of. While trying to prove this I stumbled on this interesting polynomial identity:. Looks similar to the binomial coefficient. Is an integer for integer values of. To use this identity for the problem at hand, we first note that setting. Is an...
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Bedtime mathematics – Page 2 – Mathematics that is slept on…
https://mymbl.wordpress.com/page/2
Mathematics that is slept on…. What to expect in here. Another nugget concerning cyclotomic polynomials. April 26, 2011. In our build up to a proof of this problem., we established that the product is a multiple of each of the numbers for . But we wished to show the stronger result that is divisible by . One way to proceed to estimate how the lcm, differs from the product and see if also… More another nugget concerning cyclotomic polynomials. Another nugget concerning cyclotomic polynomials. Let A and B ...
