Evaluate Function - update

Previous post
The evaluate function described in the previous post has been used in writing a UDF that will evaluate the integral of any suitable function over a specified range.
The revised worksheet can be downloaded from:
Eval.zip

Elegant proofs 2 - The area of a circle

We are so familiar with the formula for the area enclosed by a circle that we tend not to think much about how it was derived, at least I don’t.
The proofs of the formula are in fact many and varied; the first one found by Google is at:
http://www.artofproblemsolving.com/LaTeX/Examples/AreaOfACircle.pdf
Don’t worry, that’s not the elegant one.
There are [...]

Pythagoras, Penrose and Pov-Ray

Images based on Pythagorean tiling, Penrose tiling, and projections onto the Riemann Sphere by PM2ring, a regular contributor to the ABC Self-Service Science Forum (words by the artist):
 Various renderings of a Pythagorean tiling. Mostly using the 3,4,5 triangle. This tiling has been called a “wordless proof” of Pythagoras’ Theorem. It shows by dissection that the [...]

Irish Graffiti

On the 16th October 1843 the Irish mathematician William Hamilton was taking a walk with his wife, alongside the Royal Canal in Dublin, when the answer to a problem that he had been puzzling over came to him, and he was so excited by this discovery that he carved the equation:
I2 = j2 = k2 [...]

The roof of the Taq-i-Kisra; Analysis

Following the previous post, I have compared the stresses in the Taq-i-Kisra assuming either a catenary or parabolic profile. I have also compared constant depth sections with sections increasing in depth towards the supports. The arch span was taken as 24 metres, with an arch height of 16.6 metres, supported on vertical faced [...]

Elegant Proofs - 1

Roger Penrose in his book “The Road to Reality” gives a remarkably simple proof of Pythagoras’ Theorem:

Drawing a perpendicular to the hypotenuse from the right angle (line CD) will divide any right angled triangle into two similar triangles, both of which are similar to the original triangle. Since the area of similar shapes are proportional [...]

Evaluate Function

It would often be convenient to evaluate a function entered as text; for instance if we have the function for the deflection of a cantilever under point loading at the end:
F*L^3/(3*E*I)
then it would be convenient to be able to allocate different values to F, L, E and I, and calculate the value of the function, [...]

Section Properties of Defined Shapes - Spreadsheet

Download section properties spreadsheet from:
http://www.interactiveds.com.au/software/Section%20Properties03.zip
http://www.interactiveds.com.au/software/Section%20Properties07.zip

Section properties for 35 defined shapes

Section properties from coordinates

Section properties UDF

Screen shots:

Section Properties from Layers

An alternative to finding the section properties of irregular polygons from the coordinates of the corners is to divide the shape into rectangular or trapezoidal layers.  The properties of the shape may then be found by simply summing the properties of each layer about a common axis.  The applicable equations for rectangular and trapezoidal layers [...]

Section Properties from Coordinates

The area of irregular closed polygons defined by coordinates may be conveniently calculated by summing the areas of adjacent trapeziums, as shown below.   The area of each trapezium is calculated from the X axis.  Note that with the apex coordinates defined in a clockwise direction the area between the bottom of the polygon and the [...]