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Viewing entries tagged Math

Birth Certificate of America?

Posted by Diego Fonstad
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on Wednesday, 04 July 2012
in Images that speak for themselves

waldseemuller mapTeachable Moment: This >500 year old image raises the age old question of credit in discovery: what does it mean to be the first person to document what others know.  The high resolution image can also be printed and cut out as a lesson in how to project a sphere onto a flat surface.

In 1507, German cartographer Martin Waldseemüller made the first known maps naming America.  In 2007 Germany gifted one of the known versions of this map to the Libray of Congress calling it the "Birth Certificate of America."  Recently, another copy was discovered and was "released" by the Ludwig-Maximilians-Universität (LMU) München on the Internet on July 4, 2012.  Here's a link to the high resolution PDF: http://epub.ub.uni-muenchen.de/13138/1/Cim._107-2.pdf

For the press release and more pictures go here: http://www.en.uni-muenchen.de/news/newsarchiv/2012/spotlight/tdw_ub_fund.html

Tags: Math, Random
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How much water is there on earth?

Posted by Diego Fonstad
Diego Fonstad
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on Tuesday, 19 June 2012
in Images that speak for themselves

water on earthTeachable Moment: This stunning image from the USGS illustrates shows both the relative scarcity of water on our planet and challenges our thinking of volume.  We all know that the earth is almost 97% covered with water, but how many of us realized how thin a layer that represented and what that was relative to the land mass?  Follow the link to a larger image and the underyling math.

Reference: http://ga.water.usgs.gov/edu/2010/gallery/global-water-volume.html

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Science Friday

Posted by Diego Fonstad
Diego Fonstad
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on Thursday, 14 June 2012
in Online Resources

scifriTeachable Moment: NPR's Science Friday is a great show exploring math and science and their web site is a wonderfully rich resource not only for listening to older episodes but also for finding engaging videos and teacher tools.

Science Friday is a weekly science talk show, broadcast live over public radio stations nationwide from 2-4pm Eastern time as part of NPR's 'Talk of the Nation' programming. Each week, we focus on science topics that are in the news and try to bring an educated, balanced discussion to bear on the scientific issues at hand. Panels of expert guests join Science Friday's host, Ira Flatow, a veteran science journalist, to discuss science - and to take questions from listeners during the call-in portion of the program.

Reference: http://www.sciencefriday.com/

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Measuring the Universe

Posted by Diego Fonstad
Diego Fonstad
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on Thursday, 14 June 2012
in Videos worth watching

measure the universe250Teachable Moment: This brilliant little video made by the Royal Observatory in Greenwich covers the concepts of parallax, doppler and red-shift and shows how they are all used together to measure the universe.

 

 

 

Hits: 17253

Visual proof of Area of a Circle

Posted by Diego Fonstad
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on Wednesday, 13 June 2012
in Videos worth watching

 Teachable Moment: Simple little visual proof of the formula for the area of a circle. 

 

Tags: Math
Hits: 11042

Trick for teaching basic trigonometry

Posted by Diego Fonstad
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on Monday, 11 June 2012
in Great Explanations

Teachable Moment: Nice simple and straight forward trick to remember 

From the Blog:

"During my middle-school teaching days I noticed that often kids would arrive in my 8th-grade class with a half knowledge of sine, cosine, tangent. There were two major problems they often had in solving for unknown sides in a right triangle using trig:

1. They couldn't visually distinguish opposite side vs. adjacent side. Many middle-schoolers I taught had a poor consistency (if any) with recognizing what "opposite" and "adjacent" meant in a diagram; it was just too abstract for them, even though I tried to explain how to look for the sides "across" the triangle, etc.

2. They couldn't figure out whether to use sine, cosine, or tangent in a given situation.

Follow the link below to read more. 

Reference: http://untilnextstop.blogspot.com/2011/02/trick-for-teaching-basic-trig.html

Tags: Math
Hits: 109782

Mudd Math Fun Facts

Posted by Diego Fonstad
Diego Fonstad
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on Sunday, 10 June 2012
in Online Resources

Teachable Moment: Nice little collection of math facts curated by a Harvey Mudd math professor...

I developed Math Fun Facts in 1994 as a warm-up activity for the calculus courses I taught as a graduate student at Harvard. Calculus was the final math course that most of my students would take, and I worried that they would emerge from college with the mistaken notion that all of mathematics was "just more calculus". Most college students never see the interesting stuff that motivates mathematicians to study the subject.

So, I began to tell them "Fun Facts"---daily mathematical tidbits from all areas of mathematics (not just calculus), meant to arouse their curiosity and fascination with the subject. Fun Facts give students a glimpse that mathematics is full of interesting ideas, patterns, and new modes of thinking.

The student reaction to Fun Facts was highly positive. Once I started, I couldn't stop---students would clamor for them if I forgot to give one. They stopped me after class to discuss them, began to create their own, and were motivated to take other math courses because of the Fun Facts they learned.

I got the idea from something that one of my college professors (John Jones) did; he once wrote an interesting infinite series on the board and called it a "fun fact". I thought to myself: why not do something like this everyday and include brief fun facts from all areas of mathematics? I told myself that if I became a professor someday, I would try it...

So here, on this site, is an archive of many of the Fun Facts that my colleagues and I have collected. I launched this site on July 20, 1999 so that others might use it as a resource and repository of ideas, and it continues to grow. I hope you enjoy this site... do feel free to visit often!

Reference: http://www.math.hmc.edu/funfacts/about.shtml

Tags: Math
Hits: 22827

Visualization of pi to 4,000,000 decimals

Posted by Diego Fonstad
Diego Fonstad
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on Sunday, 10 June 2012
in Images that speak for themselves

Teachable Moment: This is a beautiful and creative way of illustrating Pi.  

An average person can read out approximately 120 digits/min.  Keeping this pace it would take more than 158,000 years to recite the 10 trillion digits discovered this year and roughly 3 weeks to read out the 4 million digits visualized here.

Tags: Math
Hits: 18033

MIT +K12

Posted by Diego Fonstad
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on Saturday, 09 June 2012
in Online Resources

Teachable Moment: Sometimes the best person to teach a challenging concept is someone who has recently learned it and wants to share their own excitment of the discovery. I can't wait to see this video library grow.

 

MIT has launched an initiative encouraging its students to produce short videos teaching basic concepts in science and engineering. The videos — aimed at younger students, in grades from kindergarten through high school — will be accessible through a dedicated MIT website and YouTube channel. A subset of the videos will also be available on Khan Academy, a popular not-for-profit educational site founded by an MIT alumnus.

References: http://k12videos.mit.edu/

Hits: 21352

Seven Equations that Rule Your World

Posted by Diego Fonstad
Diego Fonstad
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on Monday, 26 March 2012
in Videos worth watching

Equations that Rule your World logoTeachable Moment: This is a great synthesis of how a series of clearly important, yet seemingly disparate, equations have been used together to provide us modern conveniences.

Without equations, most of our technology would never have been invented. Of course, important inventions such as fire and the wheel came about without any mathematical knowledge. Yet without equations we would be stuck in a medieval world.

Hits: 23601

Einstein Archives Online

Posted by Diego Fonstad
Diego Fonstad
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on Monday, 19 March 2012
in Images that speak for themselves

Teachable Moment: Anyone interested in history of science would love these archives.  From his notes deriving his famous equation to his love letters this is a treasure trove of information that humanizes this great scientist.

The Einstein Archives Online Website provides the first online access to Albert Einstein’s scientific and non-scientific manuscripts held by the Albert Einstein Archives at the Hebrew University of Jerusalem, constituting the material record of one of the most influential intellects in the modern era. It also enables access to the Einstein Archive Database, a comprehensive source of information on all items in the Albert Einstein Archives.

DIGITIZED MANUSCRIPTS

From 2003 to 2011, the site included approximately 3,000 high-quality digitized images of Einstein’s writings. This digitization of more than 900 documents written by Einstein was made possible by generous grants from the David and Fela Shapell family of Los Angeles. As of 2012, the site will enable free viewing and browsing of approximately 7,000 high-quality digitized images of Einstein’s writings. The digitization of close to 2,000 documents written by Einstein was produced by the Albert Einstein Archives Digitization Project and was made possible by the generous contribution of the Polonsky Foundation. The digitization  project will continue throughout 2012.

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Posted by Diego Fonstad
Diego Fonstad
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on Thursday, 01 March 2012
in Videos worth watching

Hans Rosling's 200 Countries, 200 Years, 4 MinutesTeachable Moment: I have always been a sucker for good visualization but this visualization of 120,000 numbers plotted in a dynamic and interactive narrative opens the mind to the possibilities in visualization.

Hans Rosling's famous lectures combine enormous quantities of public data with a sport's commentator's style to reveal the story of the world's past, present and future development. Now he explores stats in a way he has never done before - using augmented reality animation. In this spectacular section of 'The Joy of Stats' he tells the story of the world in 200 countries over 200 years using 120,000 numbers - in just four minutes. Plotting life expectancy against income for every country since 1810, Hans shows how the world we live in is radically different from the world most of us imagine.

Tags: Math
Hits: 33425

Interactive Scale of the Universe

Posted by Jennifer
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on Wednesday, 29 February 2012
in Images that speak for themselves


interactive scaleTeachable Moment:
This interactive website allows kids and adults to explore the scale of the universe from 10 27th power to 10to the -35th power. I love the fact that objects of the same scale are compared. Who knew that Halley's Comet was about the size of Mount Everest? Or that Ganymede was larger than Mars?

Hits: 37978

Instructables

Posted by Diego Fonstad
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on Thursday, 09 February 2012
in Online Resources

Teachable Moment: I love this web site for ideas of projects to show students.  The philosophy of open source and the clarity of the instructions make this an indispensable resource for great STEM projects.

Instructables is a web-based documentation platform where passionate people share what they do and how they do it, and learn from and collaborate with others. The seeds of Instructables germinated at the MIT Media Lab as the future founders of Squid Labs built places to share their projects and help others.

References: http://www.instructables.com

Hits: 46159

Science Buddies

Posted by Diego Fonstad
Diego Fonstad
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on Thursday, 09 February 2012
in Online Resources

Teachable Moment: Great resource for ideas for science projects.

Science Buddies mission is to help students from all walks of life to build their literacy in science and technology so they can become productive and engaged citizens in the 21st century. We have created personalized learning tools, over 15,000 pages of scientist-developed subject matter (including experiments based on the latest academic research), and an online community of science professionals who volunteer to advise students. We also provide resources to support parents and teachers as they guide students doing hands-on science projects. Representing much more than a website, Science Buddies quickly and efficiently matches students with the information that will hold their interest and answer their questions. We provide a bridge between scientists and students, giving students access to current scientific research and simultaneously giving scientists a way to reach out to young people interested in their fields.

References: http://www.sciencebuddies.org/

Philip Glass - Sesame Street - Geometry of Circles

Posted by Diego Fonstad
Diego Fonstad
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on Monday, 06 February 2012
in Videos worth watching

Philip Glass Geometry of Circles Sesame StreetTeachable Moment: Circles have so many fun properties and are a great way of introducing basic geometric shapes.

"Geometry of Circles" is a series of unnumbered animation pieces created for Sesame Street in 1979. Cathryn Aison commissioned Philip Glass to write music for animation based on her storyboard which had been submitted to and approved by Edith Zornow of CTW.

Tags: Math
Hits: 25631

Pasta Geometries

Posted by Diego Fonstad
Diego Fonstad
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on Tuesday, 24 January 2012
in Favorite Books

Teachable Moment: At first glance, books like this may seem excessive and exaggerated attempts to tease math out of every day objects, but in an era of graphing calculators, math based 3D modeling tools like OpenScad, and vector based drawing tools, books like this provide a great, real world relevance to the underlying math behind complex shapes. It doesn't hurt that it beautifully put together.

Tags: Math

Mathematics Genealogy Project

Posted by Diego Fonstad
Diego Fonstad
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on Wednesday, 19 October 2011
in Online Resources

Teachable Moment: Isaac Newton famously said he'd seen further because he'd stood on the shoulders of giants and this project is a great way of illustrating the interconnected nature of learning and advancements.

Mission Statement

The intent of this project is to compile information about ALL the mathematicians of the world. We earnestly solicit information from all schools who participate in the development of research level mathematics and from all individuals who may know desired information.

Tags: Math
Hits: 12899

Cool math trick: Converting between miles and kilometers

Posted by Diego Fonstad
Diego Fonstad
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on Monday, 12 September 2011
in Great Explanations

Teachable Moment: The Fibonacci sequence is a great introduction to math in nature and this little trick even provides a nifty practical use of the numbers.

From the blog: "The Fibonacci sequence is made up of numbers that are the sum of the previous two numbers in the sequence, starting with 0 and 1. It's 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… 1 is 0+1, 2 is 1+1, 3 is 1+12, 5 is 2+3, and 8 is 3+5. The number after 144 is 233, or 89+144. The Fibonacci number describes the golden spiral, an ideal form much beloved by designers everywhere. Interestingly, it also neatly matches the relationship between kilometers and miles. Three miles is five kilometers, five miles is eight kilometers, eight miles is 13 kilometers. It's not perfect, eight miles is actually 12.875 kilometers, but it's close enough in a pinch. If you need to convert a number that's not on the Fibonacci sequence, you can just break out the Fibonacci numbers, convert, and add the answers. For instance, 100 can be broken down into 89 + 8 + 3, all Fibonacci numbers. The next numbers are 144, 13, and 5, which add up to 162. 100 miles is actually equal to 160.934. Again, close enough. Math is cool."

References: http://www.mnn.com/earth-matters/wilderness-resources/blogs/cool-math-trick-converting-between-miles-and-kilometers

Tags: Math
Hits: 52784

Information is Beautiful

Posted by Diego Fonstad
Diego Fonstad
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on Friday, 19 August 2011
in Online Resources

Teachable Moment: Brilliant examples of representing complex data in stunning visual ways.  This web site is a trove of ideas for students looking to best present their data in innovative ways.

I’m David McCandless, a London-based author, writer and designer. I’ve written for The Guardian, Wired and others. I’m into anything strange and interesting.

Hits: 23997