FE 'tkGooie' Utilities A Menu of Tk script CODE for some 'MATHed' educational utilities (FE = Freedom Environment)

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

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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 (and toolchests) such as 3Dtools AUDIOtools FILEmanagers IMAGEtools INTERNETtools MATHtools MATHed ODEtools Converter-SELECTORtools PHYSICStools PLOTtools SELECTORtools SYSTEMtools TEXTtools VIDEOtools Tk-GUIs EMBELLISHED demos 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.

'MATHed' Menu (List of Links to pages that present descriptions and CODE for '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_ SubtendingAngle AtCenter IsTwice AngleAtCircumference' 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 are 'the inscribed angle theorem' and '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. Ptolemy 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: An animated demo of an Asian method of showing circle area = R * circumference / 2 --- which involves rearrangement of 'pie slices' of a circle into a rectangular or triangular shape. A GUI for Animating the Summation of Various Series --- with examples from Cavalieri and Wallis, Gregory and Leibniz, Euler, etc. A GUI for Animating Convergence of Infinite Products ---- with examples from Viete, Wallis, Euler, etc. An interactive demo of a Chinese demonstration of the Pythagorean theorem, based on inscribing 4 copies of a right triangle within a square. An interactive demo of Euclid's proof of the Pythagorean theorem, based on morphing triangles into triangles of equal area (where the triangles are acutally halves of parallelograms of equal height). An interactive demo of President Garfield's proof of the Pythagorean theorem, based on inscribing 2 copies of a right triangle in a trapezoid. An interactive demo of an Egyptian method of approximating the area of a circle with a series of inscribed squares, the method of which is indicated by images here or here --- which, in turn, bring to mind the midpoint circle algorithm. An alternate method using 5 squares and 4 triangles is indicated in an image here. An interactive demo of a method to approximate the area of circle with rectangular slices --- a method that is seen in old Japanese documents. Experiments with Newton's iterative formula for calculating binomials with negative and/or fractional exponents An animation of creation of the Koch snowflake, with color and fill options. An animation of creation of the Sierpinski gasket, with color and fill options. An animation of the fact that the 3 altitude lines of any triangle meet in a common point. An animation of the fact that the 3 perpendicular-bisector lines of any triangle meet in a common point An animation of the fact that the 3 angle-biscector lines of any triangle meet in a common point. An animation of the fact that the 3 'median' lines of any triangle meet in a common point tkOscilloscope - an emulator of an oscilloscipe, to experiment with dynamically changing curves in 'the plane'. tkHarmonograph - an emulator of a harmonograph, to experiment with the types of curves that it generates. An interactive demo of using 2 triangles to multiply --- and divide and take reciprocals (a non-logarithmic sliderule) An alternative method involving connecting points of a parabolic curve with a straight line and noting where the line crosses the y-axis is here. Other similar processes can be described, for generating powers and roots geometrically, for example. An interactive demo of the Law of Cosines --- a.k.a. the 'cosine formula' or 'cosine rule'. An interactive demo of the Law of Sines. An interactive demo of the sine and cosine half-angle formulas. An interactive demo of the sine and cosine sum of angles formulas. An interactive demo of Heron's formula for the area of a triangle given the lengths of its three sides. An interactive demo of Ceva's theorem giving a relation for the ratios of lengths of 3 line-segments from vertices of a triangle, when the 3 segments have a common intersection point. An interactive demo of Pappus's hexagon theorem. An interactive demo of Desargues's theorem. An interactive demo of Morley's Trisector Theorem --- including color choices, labels, calculation of side lengths and area and angles. An interactive demo of Simson's line --- 3 co-linear points based on a triangle and its circumcircle. An interactive demo of Viviani's theorem on equilateral triangles --- the sum of the distances from any interior point to the sides of an equilateral triangle are the always equal to the altitude of the triangle. An interactive demo of Descartes' method of finding a square root via a semicircle construction. Another source of info on this method is a page at maa.org. An interactive demo of Descarte's theorem concering four 'kissing' circles. Give the user a choice of up to 100-plus point-line-circle (surprising) configurations that have been discovered for any given triangle --- examples: the 9-point circle and the Euler line. and more Some math-related Tk GUI scripts may be put in another category --- such as an 'IMAGEanimations' sub-toolchest of the 'IMAGEtools' toolchest: Simulation of wave interference patterns from waves through 2 slots Emulate Brownian motion, restricted to 2D (display polygonal track on Tk canvas) Emulate Brownian motion, polygonal tracks in 3D (with a 3D viewer, and projection of tracks on a Tk canvas) --- someday? --- OR in a 'PHYSICStools' toolchest: tkAnimateCollisionOfTwoRigidMasses_1D tkAnimateCollisionOfTwoStickingMasses_1D Other math-related Tk GUI scripts can be seen on the ODEtools page, where ODE = Ordinary Differential 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 'The Number Mysteries' (2010) and several more 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. Beckmann, Petr - 'The History of Pi' (1971) Beutelspacher, Albrecht - 'Numbers: Histories, Mysteries, Theories' (2013,2015) Chamberland, Marc - 'Single Digits: In praise of small numbers' (2015) Crilly, Tony - '50 Mathematical Ideas' (2007) Havil, Julian - 'The Irrationals' (2012) Kaplan, Robert and Ellen - 'The Art of the Infinite' (2003,2014) Lockhart, Paul - 'Measurement' (2012) Mach, Ernst - 'The Science of Mechanics' (1919, 2009) Pask, Colin - 'Great Calculations' (2015) Peterson, Ivars - 'The Mathematical Tourist' (1988,1998,2001) Stahl, Saul - 'Geometry from Euclid to Knots' (2003,2010) Weinberg, Steven - 'To Explain the World' (2015) 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 Geometry Mathematical Series Trigonometry Numerical Analysis Applied Mathematics Differential Equations Harmonic Analysis Mathematical Physics Computational Physics Mechanics Classical Mechanics Dynamics Vibrations and Waves Kinetic Theory Continuum Mechanics 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 this Menu page of Links to pages of description-and-CODE for FE 'tkGooie' scripts in the 'MATHed' group. To return to a previously visited web page location, click on the Back button of your web browser a sufficient number of times. OR, use the History-list option of your web browser. OR ... < Go to Code-Links Menu, above. > < Go to Top of Page, above. > Page history: Page was created 2014 May 05. Page was changed 2014 May 16. Page was changed 2015 Oct 05. 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.) Page was changed 2018 Aug 19. (Added css and javascript to try to handle text-size for smartphones, esp. in portrait orientation.) Page was changed 2019 Feb 24. (Minor reformatting of the page.) Page was changed 2019 Jun 13. (Specified an image width in percents to size the image according to width of the browser window.)