An old bridge in Palermo and pointed arches

The Ponte dell’ Ammiraglio (Admiral’s Bridge) in Palermo, Sicily, built from 1125-1135 (or 1113, according to the Italian Wikipedia), is one of the oldest surviving post-Roman era arch bridges in Europe.  The bridge has been restored and surrounded by a new park, but also being surrounded by busy Sicilian roads, cut off from its original purpose, and outside the main tourist area, it is little visited.

There is also little information about this bridge on the Internet (at least in English), but I did find a lengthy discussion on the history of pointed arches, and where they came from, which is well worth a read at:

Nexus Network Journal (architecture and mathematics on-line)

Thanks to the comment from Pier below, a You tube video of an event on the bridge:

Posted in Arch structures, Historic Bridges, Newton | Tagged , , , , | 2 Comments

ExcelPython2, Alglib and Spline-Matrix Rel 2.03

Following a comment here: ExcelPython2, Alglib and Spline-Matrix update I have updated the VBA and Python code, and added a missing Python module to the download zip file.  See the earlier post for details of installation and use, or download the revised files from:

xl_Spline-Matrix2.zip

The revised spreadsheet should work with 32 bit Excel, provided the instructions for installing Python (including Numpy) and Alglib are followed.

Posted in AlgLib, Excel, Link to Python, Maths, Newton, Numerical integration, NumPy and SciPy, UDFs, VBA | Tagged , , , , , , | Leave a comment

Waterspout off Taormina

Staying at the Sicilian resort town of Taormina, I have just observed the waterspout shown below:

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IMG_7604

IMG_7605

Read all about waterspouts at Wikipedia.

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Bruton Town – A very old story

Bruton Town is an English Folk song featured on The Pentangle’s first album (the first LP I ever bought).  It tells the story of a young woman whose lover is murdered by her two brothers, because they do not think him worthy of her.

According to this link the song:

 is a version of the story Isabella and the Pot of Basil, made famous by Boccaccio in The Decameron, but the ballad obviously draws on popular tradition since then. It is also known as The Bramble Briar, The Jealous Brothers, The Merchant’s Daughter, and The Murdered Servantman, and can be found in 100 English Songs, edited by Cecil Sharp who collected it in 1904.

… and the Boccaccio story, together with its link to a poem by John Keats may be found at:

Giovanni Boccaccio. The Decameron (ca. 1353)

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Binary functions, combining text, and finding unique columns

I recently had an e-mail request asking for a method of finding unique columns in an Excel table consisting of either blank cells or an entry of 1.  An easy way to do this would be to convert the columns to a binary value, then use the Countif function to count how many copies there were of each column.  Excel does not provide a convenient way to combine the contents of many cells into a single value, but a simple User Defined Function (UDF) to perform this task can be downloaded from Binary Functions.xls.

The Binary Functions spreadsheet uses code from: Visual Basic Code Examples , which provides code to convert binary to and from decimal, octal and hex values.  I have added code to create a binary value or text string from an Excel column (or row) of values.  Output from this spreadsheet is shown in the screen shot below:

BinFuncs2

 

Note that:

  • Excel has functions to convert between binary and decimal, but these are limited to a very small maximum value.
  • The BinRangeToString function assigns each cell a value of 0 for cells containing 0 or empty cells, or 1 for anything else.
  • The BinRangeToDec function returns a floating point decimal value, and will not be reliable for columns with more that 48 rows.
  • The TextString function returns a concatenated string of the contents of each cell.

The TextString function was previously presented at: Stringing more than two words together.  The TextString function has now been modified to display values formatted as “general” correctly, and to optionally allow blank cells to either be ignored, or included in the returned string.  The revised file may be downloaded from TextString.xls

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