• Free Textbooks in Mathematics

    Fri, 02/24/2017 - 08:00 — yonatan zilpa
    The following is a list of links to useful textbooks in mathematics, available for free on the Internet. All books are legally safe to download, The books are in printable format - Postscript (PS) or Portable Document Format (PDF). You are free to download, read and print them. This is a partial list of "free textbooks" in math, the list is to be updated regularly.
    Tags: 
    math textbooks

  • Four bottles - Equidistant mouth problems

    Sun, 04/17/2016 - 05:29 — yonatan zilpa
    How to place four identical bottles in the plane such that the distance between each pair of mouths will be the same?
    Tags: 
    math recriation

  • Hahn Decomposition Theorem

    Thu, 11/24/2016 - 14:07 — yonatan zilpa
    Let $\nu$ be a signed measure over measurable space $(X,\mathcal{M})$. Denote $\tilde{N}=\left\{ u\in \mathcal{M} \; :\; \mbox{$u$ is $\nu$-negative} \right\}$ and $\tilde{P}=\left\{ u\in \mathcal{M} \; :\; \mbox{$u$ is $\nu$-positive} \right\}$
    1.   $\exists N\in \tilde{N}\Big(\exists P \in \tilde{P}\Big( N\cap P=\emptyset \; \mbox{ and }\; N\cup P = X\Big)\Big)$
    2.   $\forall N,N^{'}\in \tilde{N}\Big(\forall P,P^{'}\in \tilde{P} \Big(N\sqcup P =N^{'}\sqcup P^{'}=X \; \Longrightarrow \nu( P\triangle \tilde{P})=\nu( N\triangle \tilde{N})=0\Big)\Big) $
    Tags: 
    theorems

  • How many squares can be found here?

    Sun, 08/14/2016 - 13:40 — yonatan zilpa

    How many squares can be found here?
    Tags: 
    recreational mathematics

  • Asymptotic Differentiable Function

    Thu, 11/24/2016 - 14:45 — yonatan zilpa
    Let $f$ be any function asymptotic at zero. Prove/Disprove:
    If $f$ is differentiable everywhere in its domain, then $\lim_{x\to \infty}f\;'(x)$ must be equal to zero?
    Tags: 
    recreational mathematics

  • Conceptual Language and Learning

    Mon, 12/26/2016 - 15:17 — yonatan zilpa
    Normally when we learn human spoken language we translate words to our own mother tongue language. But when we learn our mother tongue language we have no language to translate new words. How do we understand mother tongue without translating words? Is there some kind of conceptual language where we can translate mother tongue new words? And if so, can we use this conceptual language to become better learner?

    concept map

    Tags: 
    learning tips

  • Fibonacci Sequence, A Pattern of Natural Beauty

    Fri, 02/26/2016 - 17:33 — yonatan zilpa
    The sequence of Fibonacci can be found everywhere in nature. First mentioned by Leonardo Fibonacci who was a medieval mathematician that was trying to solve problem involving the growth of a population of rabbits. It became one of the most famous sequence in all of mathematics. Here is a mathematical description of some of its fundamental properties...
    Fibonnaci as appeared in a snail
    Tags: 
    recreational mathematics

  • List of Computer tools in mathematics

    Fri, 02/26/2016 - 16:53 — yonatan zilpa
    The following list links to free computer tools for mathematics.

  • Emotions Relationship & Learning

    Wed, 12/07/2016 - 14:48 — yonatan zilpa
    It's been said that "necessity is the mother of inventions", but necessity is the mother of learning as well. Learning is vital to survival it is a necessity, however necessity determines what we learn. This interaction between necessity and learning is part of "emotional relationship" between the learner his/her topic.
    Tags: 
    learning tips

  • The circle of Apollonius

    Fri, 02/26/2016 - 17:05 — yonatan zilpa
    By definition, a circle is the locus of all points equidistant from a fixed center. However, the circle of Apollonius is defined differently. In the following post I will define and construct an Apollonian circle.
    Tags: 
    geometry

Pages

Subscribe to Front page feed