Math: Density Plots of Trig Expressions. old. repost.

Kolam (Tamil-கோலம்) is a form of drawing that is drawn by using rice flour/chalk/chalk powder/white rock powder often using naturally/synthetically colored powders in Tamil Nadu, Karnataka, Andhra Pradhesh, Kerala and some parts of Goa, Maharashtra, Indonesia, Malaysia, Thailand and a few other Asian countries. A Kolam is a geometrical line drawing composed of curved loops, drawn around a grid pattern of dots. In South India, it is widely practised by female Hindu family members in front of their houses.[1] Kolams are regionally known by different names in India, Raangolee in Maharashtra, Aripan in Mithila , Hase and Raongoli in Kannada in Karnataka, Muggulu in Andhra Pradhesh, Golam in Kerala etc.,[2] More complex Kolams are drawn and colors are often added during holiday occasions and special events.

[2017-01-12 Kolam]

many more, see https://twitter.com/mariawirth1/status/810098967761616897

logician Raymond Smullyan is 97 now. ☹

Raymond Smullyan is famous among armature mathematicians for his many books on logic, presented as intriguing logic puzzles.

## Knights and Knaves

On a island, all inhabitants are either knights, who always tell the truth, or knaves, who always lie.

John and Bill are residents of the island.

John says: We are both knaves.

Who is what?

here's his books Raymond Smullyan books

truly amazing Euler, greatest mathematician. Here's his story told by William Dunham, 2008. Save 1 hour to watch.

the best introduction to graph theory is this one.

if you don't know the basics, get it, read it in a week, 1 hour a day. Once you start reading, you can't put it down.

Henry Segerman has been doing amazing things lately.

The story of SageMath. http://wstein.org/papers/talks/2016-06-sage-bp/bp.pdf

excellent story, if you want to know about math software, open source, academia.

here's video version.

The story of SageMath. http://wstein.org/papers/talks/2016-06-sage-bp/bp.pdf

excellent story, if you want to know about math software, open source, academia.

more about cardioid here: Cardioid

It's, BEAUTIFUL!

in my youth, i studied this game and lots similar ones. You can search wikipedia for math and books. The name is peg solitaire. Here: Peg solitaire.

You begin with a configuration where there's a hole in the center, while all other are filled with marbles (or called pegs). You can remove a peg by jumping one over it. The goal is to leave just 1 peg on the board.

〔The Involute of a Cubical Parabola By John Baez. @ https://johncarlosbaez.wordpress.com/2016/03/22/the-involute-of-a-cubical-parabola/〕

〔The Capricornoid By John Baez. @ https://johncarlosbaez.wordpress.com/2016/03/06/the-capricornoid/〕

looks like Geometer's Sketchpad is now free. Download at http://www.keycurriculum.com/

That's really one chapter of history.

Geometer's Sketchpad was revolutionary in math education, in the 1990s. And, it was very popular. I believe there are also 1 or more Euclidean geometry theorem discovered due to use of such software, but i couldn't find a citation at the moment. But since 2000, many many interactive plane geometry came up. By 2010, it's a dime a dozen, most are free. Most popular is the open souce GeoGebra. (http://www.geogebra.org/) 〔➤see Great Software for Plane Geometry〕

For history of Geometer's Sketchpad, see http://www.dynamicgeometry.com/General_Resources/The_Sketchpad_Story.html

Apparently, the company is acquired.

## McGraw-Hill Education acquires Key Curriculum

Aug 2, 2012

KEY CURRICULUM: Acquired by McGraw-Hill Education for an undisclosed amount. The Emeryville, CA-based publisher built its brand over the past decades with a series of math texts and materials, along with digital tools like Geometer's Sketchpad and TinkerPlots. But recent years found the print business struggling, leading to a series of layoffs and restructuring to re-focus on its digital offerings. McGraw-Hill, no stranger to dire straits, hopes these tools can jumpstart its own business.

[source: https://www.edsurge.com/news/mcgraw-hill-education-acquires-key-curriculum]

Nicholas Jackiw, who wrote Geometer's Sketchpad, seems now work for SRI International.

Nicholas Jackiw

Senior Research Scientist, Center for Technology in Learning

Nicholas Jackiw is a senior research scientist in SRI International’s Center for Technology in Learning, where his interests focus on how digital technologies can uniquely shape mathematical propositions and learners’ intellectual and material interactions with them.

His research focuses on how mathematical ideas are embedded in, and functions of, the cultural practices and representational technologies of the contexts in which they arise; and also on how new technologies and practices imply not just new mathematical representations but fundamentally new mathematical ideas and approaches. That research informs his design and development of new learning experiences, situations, and technologies.

Jackiw is the original designer of The Geometer’s Sketchpad, one of the most widely-used, regarded and emulated software tools in education. For 25 years before joining SRI, Jackiw led ongoing Sketchpad research and design at Key Curriculum Press/KCP Technologies, and coordinated Dynamic Geometry implementation projects with institutional partners around the globe.

Well. Go Download at http://www.keycurriculum.com/, and you can use the 80 GSP files at Visual Dictionary of Special Plane Curves. For example, many on this page: Deltoid

Plane Curves: GeoGebra Files Index

update complete. There are 60 of them. Enjoy!

following are interactive geometry of plane curves.

- 5-Point Conics
- Archimedean spiral
- Archimedes Circle
- Inversion of Archimedes's spiral
- Astroid Construction
- Astroid Construction
- Astroid's Pedal Curve
- Astroid Roll
- Astroid Trammel

They are GeoGebra software. Google no longer supports Java Applets. I'm updating them to html5 so they run in your browser. There are about 50 more to do, i'll be posting them in next few days. Hope you like them.

been working on Geometry: Plane Tiling Mathematica Package

for illustration at the Nature of Associative Property of Algebra

beautiful images of Barth Sextic

〈The Symmetries of Things〉 by John H. Conway (Author), Heidi Burgiel (Author), Chaim Goodman-Strauss (Author) amazon

John H Conway's ~~new~~ old book

Craig S Kaplan is a expert at mathematical decorative patterns. You can find more of his work on his site at http://isohedral.ca/

〔Computer Generated Islamic Star Patterns By Craig S Kaplan. @ http://vismath4.tripod.com/kaplan/index.html〕

visual proofs is such that we have to artfully distribute the errors all over, so that in the limit, the error disappears!

John Baez again, from which i learned about the term “rectification” (of regular polyhedron), and also read what's archimedean solid, and learned about this strange beast Elongated square gyrobicupola.

the Elongated square gyrobicupola is interesting, besides the name, because

It is sometimes considered to be an Archimedean solid, because its faces consist of regular polygons that meet in the same pattern at each of its vertices. However, unlike the rest of the Archimedean solids, it lacks a set of global symmetries that take every vertex to every other vertex.

see Baez's article here: 〔Rectified Truncated Icosahedron By John Baez. @ http://blogs.ams.org/visualinsight/2016/04/01/rectified_truncated_icosahedron/〕

by the way, i highly recommend this software KaleidoTile. See Great Math Software: Polyhedrons ＆ Polytopes

In computational geometry, the Bentley–Ottmann algorithm is a sweep line algorithm for listing all crossings in a set of line segments. Wikipedia Bentley–Ottmann algorithm

beautiful internactive demo (JavaScript) by Adam Pearce http://bl.ocks.org/1wheel/464141fe9b940153e636

Soundararajan was drawn to study consecutive primes after hearing a lecture at Stanford by the mathematician Tadashi Tokieda, of the University of Cambridge, in which he mentioned a counterintuitive property of coin-tossing: If Alice tosses a coin until she sees a head followed by a tail, and Bob tosses a coin until he sees two heads in a row, then on average, Alice will require four tosses while Bob will require six tosses (try this at home!), even though head-tail and head-head have an equal chance of appearing after two coin tosses.

〔Mathematicians Discover Prime Conspiracy. A previously unnoticed property of prime numbers seems to violate a longstanding assumption about how they behave. By Erica Klarreich. @ https://www.quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/〕

see also

- 〔Biases between consecutive primes By Terence Tao. @ https://terrytao.wordpress.com/2016/03/14/biases-between-consecutive-primes/〕
- 〔Unexpected biases in the distribution of consecutive primes By Robert J Lemke Oliver And Kannan Soundararajan. @ http://arxiv.org/abs/1603.03720〕

Mathematician John Baez, and expert of category theory (and quantum mechanics), has a blog about it his course of category theory, at http://math.ucr.edu/home/baez/qg-winter2016/

in particular, he highly recommend this free book on category theory.

Emily Riehl, Category Theory in Context, 2014. Emily_Riehl__Category_Theory_in_Context_2014.pdf