Mini-tours of India 4

Bundi is a town in the Hadoti region of Rajasthan state. It is of particular architectural note for its ornate forts, palaces, and stepwell reservoirs known as baoris:

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Mini-tours of India 3

Ranthambhore National Park is home to 73 Bengal tigers, and is a popular place in India to see these animals in their natural jungle habitat, but on our visit they all stayed well away from our route. Fortunately there is a wide variety of other wildlife to see:

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Mini-tours of India 2

The small city (by Indian standards) of Karauli lies to the South-East of Agra in the state of Rajasthan.  The city contains a royal palace, parts dating back to the 14th Century, which despite not getting a mention in Wikipedia, is well worth a visit:

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Mini-tours of India – 1

Following a 17 day tour of the Rajasthan region of India, the next few days will feature selected photographs of the places visited on route, starting with the city  of Agra, the Agra Fort, and the Taj Mahal:

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Sydney Opera House: the designs that didn’t make it

From the Guardian:

In 1956, the New South Wales premier Joseph Cahill announced a competition – open to anyone – to design a national opera house at Bennelong Point in Sydney. There were more than 200 entries and the eventual winner, Jørn Utzon’s concrete shells, took 17 years to realise. But what of the designs that didn’t make the cut? UK-based creative studio NeoMan were commissioned by Budget Direct to research and render seven of those entries, working with Venezuelan architecture specialists Projection Comunicación Arquitectónica to produce the final images, republished with permission below.

All seven at:

Sydney Opera  House Alternatives

 

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Multiple Integration with Scipy

Scipy has 3 functions for multiple numerical integration in the scipy.integrate module:

  • dblquad: Compute a double integral.
  • tplquad: Compute a triple integral’
  • nquad: Integration over multiple variables.

I have written six functions to call these functions from Excel, via Pyxll:

Each of the Python functions can be called to evaluate the integrals of either a function entered as a string on the spreadsheet (py_DblQuadS, py_TplQuadS, or py_NQuadS), or a Python function (py_DblQuadF, py_TplQuadF, or py_NQuadF).

The integration limits are passed as either two or three two-column ranges for the dblquad and tplquad functions, or an n-row, two-column range for nquad functions.  Note that the order of the limits is different for nquad to the dblquad and tplquad functions:

The two screen shots below show output from dblquad and tplquad on the left, and nquad on the right, with an example of the “S” and “F” function in each case,  Click on the images for full-size view:

Other significant differences between the functions are:

  • For the dblquad and tplquad functions, the variables must be x, y, and z, which are passed in the order z, y, x.  For the nquad functions the variable names are an input argument, and they are passed in the order listed.
  • Where one or both limits for the nquad functions is a formula the limits are entered in one cell in the format: [lower limit or function, upper limit or function].  See examples in the screenshots.

A Pyxll based Excel-Scipy application including these functions, and many others, will be published in the near future.

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Another (very slow) way of computing pi

The previous post included 100 Python code one-liners for calculating pi that recalculates in a fraction of a second.  The video below shows an alternative approach that is a little slower:

How much slower?  If you had a computer that would do 1 million collision calculations per second, and you ran it for about 10 billion years, you could calculate pi to just 23 decimal places.

What makes this interesting is not its practical value, but why it works at all:

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