My New Calculator

I bought a new handheld calculator!Curta-1

Actually, it is not new; it was made about 1965. It is a Curta Type I.

Curta calculators were invented by Curt Herzstark (1902 – 1988) who, according to Wikipedia:

… was born in Vienna, the son of Marie and Samuel Jakob Herzstark. His father was Jewish and his mother, born a Catholic, converted to Lutheranism and raised Herzstark Lutheran.[1][2] In 1938, while he was technical manager of his father’s company Rechenmaschinenwerk AUSTRIA Herzstark & Co., Herzstark had already completed the design, but could not manufacture it due to the Nazi German annexation of Austria. … perhaps influenced by the fact that his father was a liberal Jew, the Nazis arrested him for “helping Jews and subversive elements” and “indecent contacts with Aryan women” and sent him to the Buchenwald concentration camp. However, the reports of the army about the precision-production of the firm AUSTRIA and especially about the technical expertise of Herzstark led the Nazis to treat him as an “intelligence-slave”.… he was called to work in the factory linked to the camp…. There he was ordered to make a drawing of the construction of his calculator, so that the Nazis could ultimately give the machine to the Führer as a gift after the successful end of the war. The preferential treatment this allowed ensured that he survived his stay at Buchenwald until the camp’s liberation in 1945, by which time he had redrawn the complete construction from memory.[3]

After the war he moved to Liechtenstein. In 1947 they started building and selling the calculators. Production continued until 1971 when handheld electronic calculators became widely available. In that time 79,572 Type I and 61,660 Type II machines were built. The Type II calculators have an additional two figures accuracy.

The calculator, which has about 600 parts, is based in the stepped cylinder (also called the Leibniz wheel) invented by Gottfried Wilhelm Leibniz who, as I recall, also did some work in calculus. The stepped cylinder has been used in calculating machines since Leibniz’s time.

Here is an excellent video animation explaining how the calculator works.

Of course all it does is add. Subtraction is accomplished using nines complement arithmetic, Since multiplication is repeated addition and division is repeated subtraction, it can also do those operations. But then things get interesting. There are lots of other arithmetic operations that can be done on a Curta calculator. They make use of various numerical algorithms for engineering, and business applications. If you are interested in more about this click here. For a quick example, the video below shows how to calculate square roots on a Curta using the idea that the square of any positive integer, n, is the sum of the first n odd integers, {{n}^{2}}=1+3+5+\cdots +\left( 2n-1 \right)  There are actually several algorithms for square roots and others for cube roots.

There is a Curta Calculator website. Here you will find lots of information about the Curta calculators including technical information and drawings, historical material, pictures, articles, simulators, cleaning and repair instructions, photos and videos.

Now, if I could just figure out where the batteries go….

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February 2015

 Calculus Teacher Makes the Big Times

Yitang Zhang

Photo by Peter Bohler – The New Yorker, February 2, 2015

Before turning to this month’s posts, I thought you might be interested in this. There is an interesting profile of Yitang Zhang in this week’s The New Yorker magazine by Alex Wilkinson. Mr. Zhang is a mathematician whose interest is “bound gaps” a problem in number theory on prime numbers. He is a part-time calculus teacher at the University of New Hampshire. He has won several prizes including a MacArthur award.

The profile is entitled The Pursuit if Beauty.

Wilkinson also made a short video explaining the “bound gaps” problem.


February

This month our previous posts finish a series on accumulation started in January and includes notes on power series. I have a few new post planned for February. Towards of the end of the month I plan to post a list of the previous posts on reviewing for the AP exams. As usual the four posts directly below are the most popular from previous Februarys. The most popular by a factor of about 50 (really) is the one on Error Bounds followed by iPads.

As always, please feel free to comment, question, or ask questions. I can use some suggestions about what you would like me to write about. My email address is lnmcmullin@aol.com. Notice, I’m a natural logarithm.

Thanks in advance.

Posts from past Februarys

February 2, 2013: Accumulation and Differential Equations Accumulation 6: Differential equations 

February 4, 2013: Painting a Point Accumulation 7: An application (of paint) 

February 8, 2013: Introducing Power Series 1

February 11, 2013: Introducing Power Series 2

February 13, 2013: Introducing Power Series 3

February 15, 2013 New Series from Old 1

February 18, 2013: New Series from Old 2

February 20, 2013: New Series from Old 3

February 22, 2013: Error Bounds

February 17, 2014  iPads

January

Happy New Year!

The January posts from past years finish the methods of integration thread from December and then go onto applications of integration: area between graphs, volume, and average value of a function. The month ends with a series on accumulation and functions defined by integrals.These run into February, so I’ve included them in the list below.

The most popular post from past Januarys by far is the AP Accumulation Question post. It is in the featured list below along with some others from past Januarys.

Later this month look for a new series of post on differential equations

January 2, 2013 Integration by Parts – 1

January 4, 2013 Integration by Parts – 2

January 7, 2013 Area Between Curves

January 9, 2013 Volume of Solids with Regular Cross-sections

January 11, 2013 Volumes of Revolution

January 14, 2013 Why You Never Need Cylindrical Shells

January 16, 2013 Average Value of a Function

January 19, 2013 Most Triangles are Obtuse! What is the probability that a triangle picked at random will be acute? An average value problem.

January 21, 2103 Accumulation: Need an Amount? Accumulation 1: If you need an amount, look around for a rate to integrate.

January 23, 2013 AP Accumulation Questions Accumulation 2: AP Exam Rate/Accumulation Questions

January 25, 2014 Improper Integrals and Proper Areas

January 26, 2013 Graphing with Accumulation 1 Accumulation 3: Graphing Ideas in Accumulation – Increasing and decreasing

January 28, 2013 Graphing with Accumulation: Accumulation 4: Graphing Ideas in Accumulation – Concavity

January 30, 2013 Stamp Out Slope-intercept Form! Accumulation 5: Lines

February 2, 2013: Accumulation and Differential Equations Accumulation 6: Differential equations

February 4, 2013: Painting a Point Accumulation 7: An application (of paint)

December

Which are you looking forward to more: winter vacation or teaching Riemann sums and the FTC? Well okay, vacation; me too – except that being retired is like vacation almost every day. Anyway, before vacation or certainly right after comes Riemann sums and the Fundamental Theorem, one of my favorite parts of the curriculum.

This is the list of past posts for December. There are a few new ones in the works for this year. The lead up to integration starts with three activities to get students started on integration ideas: “The Old Pump” , “Flying Into Integrationland.” and “Jobs, Jobs, Jobs.” The next four are the “featured post” below the first post on the home page; they form a series leading up to the Fundamental Theorem of Calculus. (The blog lists them automatically in most-recent-first order so I cannot change the order. Start with “Working Towards Riemann Sums” and read backwards.) Don’t skip the post “More on the FTC.”

Happy Holidays!

December: Introducing Integration, Riemann Sums, the Definite Integral, the Fundamental Theorem of Calculus, properties of integrals

November 30, 2012 The Old Pump

December 3, 2012 Flying Into Integration Land

December 5, 2012 Jobs, Jobs, Jobs

December 7, 2012 Under is a Long Way Down

December 10, 2012 Working Towards Riemann Sums

December 12, 2012 Riemann Sums

December 14, 2012 The Definition of the Definite Integral

December 17, 2012 The Fundamental Theorem of Calculus

December 19, 2012 More about the FTC

December 21, 2012 Properties of Integrals

An extra post more related to derivative applications:December 8, 2012 Inequalities

November

November – deep into derivatives. This month’s featured posts from past Novembers are below. “Speed,” which discusses various ways to approach this topic, seems to be one of the most popular with close to 2600 hits since it was first posted in 2012. This is followed by “Open cor Closed” which discusses a question that almost always comes up at workshop and online: should the interval where a function is increasing or decreasing by open or closed. The next two most popular are “Motion Problems” one of the several posts on inverses.

When I began this blog I was posting about three times per week. I have the whole of first-year calculus to write about. I hope I’ve hit the main points. If there is anything you would like me to add or expand on, or any topic or problem you think others might be interested in please let me know; I can use some ideas.

I did get a request this week to update my Guide to AP Calculus (AB & BC) Free-response Questions. (I meant to do this, but totally forgot about it.) This guide gives suggestions on what is asked on the various common free-response questions. I’ve expanded this in my posts on reviewing for the exam (check the “Thru the Year” tab under January and February). The Guide also list the question number and individual notes on individual questions from 1998 through 2014. The Guide is on the Resource page or you can click the link at the beginning of this paragraph.

Graphing, Inverses, Linear Motion, Introducing Integration

November 2, 2012 Open or Closed?

November 5, 2012 Inverses

November 7, 2012 Writing Inverses

November 9, 2012 Writing Inverses

November 12, 2012 The Calculus of Inverses

November 14, 2012 Inverses Graphically and Numerically

November 16, 2012 Motion Problems: Same Thing, Different Context.

November 19, 2012 Speed

November 21, 2012 Derivatives of Exponential Functions

November 26, 2012 Integration Itinerary

November 18, 2012 Antidifferentiation

November 30, 2012 The Old Pump

October

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School is underway and I hope things have settled down for you. You may need a little break, so I suggest you give the Calculus Humor website a look. You‘ll find some humorous things there such as the graph at the top of this post. As the name suggests they are all based on calculus.

Use the “Thru the Year” tab at the top for links to past October posts. This month has posts on the Mean Value Theorem, finding derivatives from tables and graphs, related rate problems and graphing.

The four featured posts directly below this one are the most read from past Octobers. The leader was “Reading the Derivative’s Graph” with over 6,000 hits. This was followed by “Why Radians?” with almost 3,000 hits. The two posts on Related Rates were next with an average of about 500 each.

September

Hope you all had a nice Labor Days weekend: for some a welcome day off after the first week or two of school, for others the last day of summer and back to school this week.

The four featured post below are the most popular from the August – September period.

As you know I have organized things by months and have tried to stay ahead of you so that if you find something new and useful you will have time to incorporated into you plans. If you are just starting use the August page under the “Thru the Year” tab above. If you’ve already started then look at the September guide.

Here is a series of .gifs that my son sent me that you might like Math Gifs

FoxTrot show workRevised September 1, 2014.