FE 'tkGooie' Utilities


Tk script CODE of some


educational utilities

(FE = Freedom Environment)

A hint at the method of proof.
D and E mark a square and a
rectangle with equal areas.

FE Home Page > FE Downloads Page > FE 'tkGooies' Description Page > This Page

! Preliminary ! Many more 'tkGooies' math-education scripts may be added
--- and the scripts here may be revised occasionally.

< Go to Code-Links List, below. >

OVERVIEW of 'MATHed' --- in the FE 'tkGooies' system :

A description of the FE 'tkGooies' system is available via a 'tkGooies' Description page. That page points out that the 'tkGooies' are a collection of utilities in categories (toolchests) such as

  • 3Dtools
  • AUDIOtools
  • FILEmanagers
  • IMAGEtools
  • INTERNETtools
  • MATHtools
    • MATHed
    • ODEtools
    • Converter-SELECTORtools
  • PHYSICStools
  • PLOTtools
  • SELECTORtools
  • SYSTEMtools
  • TEXTtools
  • VIDEOtools
  • Tk-GAME menus
  • Tk-WIKI demos
  • MORE

Just below is a list of links to pages that present the source code of a collection of the 'MATHed' Tk scripts in the FE 'tkGooies' system.

Many of these 'MATHed' 'tkGooie' scripts are based on theorems in plane geometry.

Some sources (books, etc.) that give ideas for 'MATHed' (math education) projects are shown in a section at the bottom of this page. These sources include equations, methods, and, in some cases, code.

List of Links to pages that present the CODE of 'MATHed' 'tkGooie' scripts:

  • Primes Sieve (in a Resizable Canvas) - a Tk GUI for showing about a million primes,
    as pixels across a canvas, with precise canvas-size control ---
    and with data for pi(N) --- the number of primes less than N

  • Thales' Theorem - Right Triangles in SemiCircle - a Tk GUI that demonstrates
    that a triangle inscribed in a semicircle is always a RIGHT triangle

  • 'tkCircleCircumferenceByPolygons' - a Tk GUI for calculating pi
    by computing circumferences of inscribed and circumscribing polygons on a circle
    (an interactive demo of Achimedes' method of approximating the circumference of a circle,
    with 'regular' polygons)

  • 'tkVarignonsTheorem' - a Tk GUI for demonstrating that
    a parallelogram is created from the 4 midpoints of ANY quadrilateral

  • 'tkNapoleonsTheorem' - a Tk GUI for demonstrating that
    an equilateral triangle is created from the 3 center-points of 3 equilateral triangles that are placed on the 3 sides of ANY triangle

  • 'tkCircleChord_SubtendingAngleAtCenterIsTwiceAngleAtCircumference' -
    a Tk GUI for demonstrating that, for a given chord (or arc) in a circle,
    the subtending angle at the center of the circle is always twice the
    subtending angle whose vertex is on the circumference of the circle.
    The nicknames for this theorem is 'the inscribed angle theorem' or
    'the central angle theorem'. This is a generalization of Thales' theorem
    (triangle inscribed in a semi-circle), above.

  • tkPtolemysTheorem_QuadrangleInCircle --- a Tk GUI for demonstrating
    that Ptolemy's equation holds no matter the configuration of a quadrangle
    inscribed in a circle.
    Ptlomemy used his equation to build a table of chords --- the forerunner of
    tables of sines of angles.

The following math-proofs-and-demos-in-Tk-GUI's are on a 'to-do' list:

Some math-related Tk GUI scripts may be put in another category --- such as an 'IMAGEanimations' sub-toolchest of the 'IMAGEtools' toolchest:

--- OR in a 'PHYSICStools' toolchest:

Other math-related Tk GUI scripts can be seen on the ODEtools page, where ODE = Ordinary Differntial Equations.

End of List of Code-Links.

How the code samples are presented :

Use the list-of-links (above) to go directly to web pages that contain source code along with code-descriptions and screenshots.

The Tk script files (and other auxiliary files, if any) are in text files that can be down-loaded to your computer and implemented.

To download, simply 'right-click' on a text link and, in a popup window of your web browser, choose an option such as 'Save Link Target As ...'.

Some SOURCES (books, etc.) for 'MATHed' coding projects:

Many ideas for 'math-ed' projects can be found in books that are meant to 'popularize' math and bring 'math surprises' to the general public --- for example, books by math-popularizers who have a Wikipedia page:

  • Bellos, Alex

    • 'The Grapes of Math' (2014) --- in England: 'Alex Through the Looking Glass'
    • 'Here's Looking at Euclid' (2010) --- in England: 'Alex's Adventures in Numberland'
  • Derbyshire, John

    • 'Prime Obssession' (2003)
    • 'Unknown Quantity' (2006)
  • Dunham, William

    • 'The Calculus Gallery' (2008)
    • 'Euler: The Master of Us All' (1999)
    • 'Journey through Genius' (1990)
    • and several more
  • Du Sautoy, Marcus

  • Maor, Eli

    • 'e: The story of a number' (1994)
    • 'Trigonometric Delights' (1998)
    • and several more
  • Nahin, Paul

    • 'In Praise of Simple Physics' (2016)
    • 'Inside Interesting Integrals' (2015)
    • 'The Logician and the Engineer' (2013)
    • 'Mrs. Perkins Electric Quilt' (2009)
    • 'Chases and Escapes' (2007,2012)
    • 'Duelling Idiots' (2000,2002)
    • and more
  • Posamentier, Alfred

    • 'Magnificent Mistakes in Mathematics' (2013)
    • 'The Secrets of Triangles' (2012)
    • 'The Glorious Golden Ratio' (2012)
    • 'The Pythagorean Theorem' (2010)
    • 'Mathematical Amazements and Surprises' (2009)
    • and many more
  • Stewart, Ian

    • 'The Mathematics of Life' (2011)
    • 'Professor Stewart's Hoard of Mathematical Treasures' (2009)
    • 'Professor Stewart's Cabinet of Mathematical Curiosities' (2008)
    • 'Taming the Infinite' (2008)
    • and many more
  • Mathematics popularizers (list at Wikipedia).

Other authors

Some books by other authors that provide 'food' for many other Tk GUI projects are as follows.

Some WebSite Sources

Some free e-books may be available from freebookcentre.net (no registration required!! no attempts to keep you on their web pages!! no annoying popups!! in 2016) --- in the areas of Mathematics and Physics --- in particular in the areas of

A similar 'free ebooks' site is at e-booksdirectory.com. See the Mathematics and Science-Physics categories.

Some 'free ebooks' and 'free HTML sites' in the math and physics categories are at physicsdatabase.com.

At 'openlibrary.org', you can use the Search field at the bottom of the math and physics pages to find books on specific topics. You can sort the results by 'most recent' (newest) or 'first published' (oldest).

Also, see the Mathematics and Physics 'bookshelves' on the Science Bookshelf page of gutenberg.org --- for some classic volumes (generally more than 80 years old).

For more sources of ideas for 'math-ed' projects, here is a page of LINKS to math web sites which includes links to math-news sites, math-blog sites, math-forum sites, math-history sites, etc.

And here is a page of LINKS to math e-documents on the web organized into categories such as Geometry, Number Theory, Algebra, Analysis (Calculus), Applied Math, Numerical Analysis, etc.

Still more ideas for 'math-ed' projects may be found via this page of LINKS to sites on science-engineering topics.

As an alternative to the several 'LINKS' sites above, here is a page that offers quick 'direct-access' to math eDocs --- 'in the public domain', mostly PDF files.

Bottom of the Links to FE 'tkGooies' Code - 'MATHed' group page.

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Page was created 2014 May 05. Page was changed 2014 May 16.
Page was changed slightly 2015 Oct 05.
Page was changed 2015 Mar 16.
Page was changed 2016 Sep 17. (Added 'tkVarignonsTheorem' page link.)
Page was changed 2016 Sep 19. (Added lots of links for 'to-do' items.)
Page was changed 2016 Oct 01. (Added the 'Sources' section.)
Page was changed 2016 Oct 02. (Added more books to the 'Sources' section.)
Page was changed 2016 Oct 04. (Added 'tkNapoleonsTheorem' page link.)
Page was changed 2017 Jan 09. (Added the 'central angle theorem' page link
    and the 'Ptolemy theorem' page link.)