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Diego Fonstad

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Blog entries tagged in Math

Birth Certificate of America?

Posted by Diego Fonstad
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

Hits: 177430

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.

 

 

 

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Visual proof of Area of a Circle

Posted by Diego Fonstad
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: 11276

Trick for teaching basic trigonometry

Posted by Diego Fonstad
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: 110633

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: 23174

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: 18410

MIT +K12

Posted by Diego Fonstad
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: 21685

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: 23966