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An interval is a connected portion of the real line. If the endpoints a and b are finite and are included, the interval is called closed and is denoted [a,b]. If the ...

The square wave, also called a pulse train, or pulse wave, is a periodic waveform consisting of instantaneous transitions between two levels. The square wave is sometimes ...

The midpoint of the first and second Brocard points Omega and Omega^'. It has equivalent triangle center functions alpha = a(b^2+c^2) (1) alpha = sin(A+omega), (2) where ...

The Randić index of a graph is defined as half the sum of the matrix elements of its Randić matrix. While the index was introduced to model the branching of the carbon-atom ...

The Gregory series is a pi formula found by Gregory and Leibniz and obtained by plugging x=1 into the Leibniz series, pi/4=sum_(k=1)^infty((-1)^(k+1))/(2k-1)=1-1/3+1/5-... ...

The parametric equations for a catenary are x = t (1) y = cosht, (2) giving the involute as x_i = t-tanht (3) y_i = secht. (4) The involute is therefore half of a tractrix.

The linear fractional transformation z|->(i-z)/(i+z) that maps the upper half-plane {z:I[z]>0} conformally onto the unit disk {z:|z|<1}.

Rings produced by cutting a strip that has been given m half twists and been re-attached into n equal strips (Ball and Coxeter 1987, pp. 127-128).

The distance from the center of a circle to its perimeter, or from the center of a sphere to its surface. The radius is equal to half the diameter.

The apodization function A(x)=(1-(x^2)/(a^2))^2. Its full width at half maximum is sqrt(4-2sqrt(2))a. Its instrument function is ...