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 [...]

Drawing in Excel - 2

Before getting down to basics, the attached file:
Animation demo
Illustrates how Excel shapes can be simply animated.
Screen shot:

The code for the animation (having previously drawn a circle and a rectangle with no fill, and noted their names):

Sub Animate()
Dim Start As Single, xInc As Single, yInc As Single, OvlWidth As Single, OvlHeight As [...]

Reinforced Concrete Section Analysis - 4

Previous post
The spreadsheet presented in the previous post in this series uses the basic equation given below to find the location of the neutral axis:
For a cross section with any applied axial load at eccentricity e, measured from the compression face, and depth of the neutral axis X below the compression face:
INA = QNA(X + e)
Where QNA [...]

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 [...]

The Roof of the Taq-i-Kisra

A higher resolution image, from a slightly different viewpoint

The roof of the Throne Room of the Taq-i-Kisra in Iran is the best surviving example of an ancient large span structure built to a catenary profile, the shape that will minimise bending moments in a structure of uniform thickness, standing under its own weight.
The red line [...]

Lane Cove Tunnel, Eastern Portal; during construction

13th July 2006.
Click on thumbnail, then click on image to see full size.

Reinforced Concrete Section Analysis - 3

Previous post -1
Previous post -2
The theory presented in the previous 2 posts in this series has been incorporated into an Excel UDF, allowing concrete and reinforcement stresses and strains to be evaluated quickly and easily for reinforced and prestressed members of complex cross-section, subject to combined bending and axial load.
The Excel file also includes UDFs [...]