# Gallery — Math

Gallery Items tagged Math

Show all Gallery Items When Area and Perimeter are “Equal”
Various geometrical shapes are described, for which the numerical value of the perimeter is the same as that of the area. Cases of one or two parameters are explored.
Rick Powers The summation of all prime numbers
A proof is given that the summation of all prime numbers can be assigned the value of 13/12, as well as values that can be assigned to the summation of all multiples and all odd multiples.
Fernando Franco Félix Journal of the French Statistical Society
This paper describes the use of the jsfds LaTeX document class and is prepared as a sample to illustrate the use of this class written for the Journal of the French Statistical Society. This an adaptation of the public document class imsart.
J-SFdS On the quantum differentiation of smooth real-valued functions
Calculating the value of Ck ∈ {1, ∞} class of smoothness real-valued function's derivative in point of R+ in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and q-difference operator. (P,q)-power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using q-difference and p,q-power difference is shown.
Kolosov Petro Sum of Squared Errors
A footnote in OpenIntro Statistics, 3rd Edition, Section 5.5.2, Analysis of Variance (ANOVA), relates an identity for the sum of squared errors (SSE).
Paul Glezen Forced Van Der Pol's Equation
This work is going to analyze the Forced Van Der Pol's Equation which is used to analyze the electric circuit. In 1927, Balthasar Van Der Pol observed the stable oscillation and heard some irregular noise in vacuum tube circuit. He then proposed the Forced Van Der Pol's Equation to analyze the circuit and suggested the concept of limit cycle and Chaos to explain his observation. In this work, We would like to analyze behavior of the model by observing the phase space, time series, bifurcation diagram and power spectrum. Those points in the figures are calculated by Runge-Kutta Method with the aid of MATLAB. For a better understanding, the RLC circuit, which is a electric circuit consisting the a resistor, an inductor and a capacitor, will be used as an example for explaining the properties. Apart from electric circuit, the Forced Van Der Pol's Equation can be applied to dynamic systems in different aspect, such as the artificial heart, economic market and so on. Therefore, we suggest this work to all students since the Forced Van Der Pol's Equation can be applied to many majors, like Mathematics, Physics, Economics, Sociology, Biology, Engineering and so on.
Wallace, Homer