Monday, October 17, 2016

Pan Balance: Cats and fractions

Usually in elementary mathematics, teaching pan scale balances are used only for display them at the time of equilibrium, to verify that two quantities are equivalent.

In this case, apart of this use, it is also useful imbalance in the balance. 

Many years ago (2003), Wendy Petti of and me, we developed the "MathCats Balance":

" choose from a wide range of objects to place on this scale - from electrons to galaxies!
" So how can we balance thin cats with fat cats? You might try multiplying each side by the number shown on the opposite side of the balance. Will 2 x 6 thin cats balance with 5 fat cats? Yes, 12 thin cats do balance with 5 fat cats".

MathCats Balance App (Google Play)
MathCats Balance (Amazon) 

Many years after this, I developed under the same idea a pan balance of fractions.
Inspired in a old photograph of Maria Montessori and his son Mario:

 ( from Getty Images: )

Pan balance to weigh fractions:

This imbalance, when the imbalance ratio under certain conditions is proportional to the ratio of content of the dishes, is also the result of the division. The slope of a straight line. In this case, the result of the division of fractions.

To view it, you can multiply the contents of each dish, until the balance is obtained, the numbers for which has multiplied each dish are in turn the result  fraction of the division.
The program only multiply by prime numbers, because any number can be built with them.

 This is the "Fractions Balance" Android App:

1/2 + 1/3 + 1/6 
with: 1/3 + 1/5 + 1/6 + 1/8 + 1/10 + 1/12
And with: 1/3 + 1/4 + 1/5 + 1/8 + 1/12

I hope it helps on teaching division of fractions.

Wednesday, October 5, 2016

Place Value Time

After the experience of my old "Time Calculator" (for 2004) I tried to develop an app that explains how this webpage subtract time.

Over the years I have received all kinds of comments on how to make this calculation.
This time, I tried to explain graphically how the original application does.

And I think I've managed to build what should have been the original application.
What was missing was to be able to modify the difference between the two dates.

(and save last configuration) 

I must thank all those who have been making comments over many years

Here you can find the new: "Place Value Time"  (for Android devices) 
(  ) 

 Here is the video of the 'Place Value Time' Android app:

 In the video:
  • - From countdown to elapsed time.
  • - my age.
  • - when I should have celebrated my 500,000 hours of life.

The app is available on Google Play, Samsung Galaxy Apps and Amazon.
Place Value Time - Google Play
Place Value Time - Amazon
Is a paid app.(the paid version of the previous 'Time Calculator' (Android)

Friday, September 16, 2016

Explore Ahmes 2/n table RMP and Akhmin n/17 table with 'Proper Fractions'

This summer, by accident I developed the 'Proper Fractions' app. (Pr.Fr. Amazon)

I was developing a new version of the 'Equivalent Fractions' But the development has been stopped for unknown reasons.
This left on my hands a circle, a square and a number line of fractions, all of them interactive.

Surprisingly for me, it proved to be very useful for exploring in unit fractions.
One issue that concerned me since I developed "Old Egyptian Fractions" for Mathcats.
I decided to do some videos to show it. It is a collection in a YouTube Playlist:

The main videos in the list:
"Explore The Ahmes 2/p table of the Rhind Mathematical Papyrus": 

Explore the Akhmim n/17 Table:

Proper Fractions It is a tool that can be useful in solving problems of Egyptian fractions:
Like the MathCats game:

More on Egyptian Fractions:
Milo Gardner:
Egyptian Unit Fractions:

I have only to add as a thank you: 
All this would not have been possible without the help and support of: +Milo Gardner (cryptanalyst)

Registered in MathTools (MathForum) 

Saturday, June 11, 2016

Exploring Mersenne primes 2^p -1

Just a note:
My app "Touch Integers ℤ (+ - × ÷)" is useful to explore the Mersenne primes:
Here there's a tiny exploration from 2^2 -1 to 2^23 -1.
We found all numbers prime, except when p==11 and p==23
Like everybody knows:

The search is made with:  "Touch Integers ℤ (+ - × ÷)" Android app:

///////     UPDATE:  (August 2016)    ////////
Same exploration on Wagstaff Prime Numbers:  

 Woodall Primes:

Euler's Lucky numbers:


And Goldbach's Conjecture:

The exploration has been made with:  "Touch Integers ℤ (+ - × ÷)" Android app:

Monday, May 23, 2016

Fluidic computers - Logic gates

In an innocent way, and mainly based on my ignorance, in 2001 I developed an online toy about building tiny computing objects with logic blocks:

Ignoring the equivalences of the Karnaugh table, OBBLOG contains all the possible logic gates with two inputs and one output.

This is the partial living OBBLOG Truth Table:

For to build a operating toy, I added forks, crossings at different levels and  bit visualizers. (Similar to a light bulb)

However, the toy did not have flip-flops, so you could not make a numbers counter, although small binary calculators 1 to 16 bits.

The toy allows to build little and simple animated toys:

Or more complex constructions:
Binary Tree:

But from the initial basic logic gates, I discovered that it was possible to build a flip-flop:
(And consequently a counter of binary numbers):
 (The obblog allows a closed loop that continues 
to circulate indefinitely if not obstructed)

Thanks to this, the obblog could become able to build calculators calculating in binary system and be able to show results in decimal system. But being only in 2 dimensions can never bequeath to do what you can get to perform with Minecraft. (Koala steamed) (see: official Minecraft logic gates)

(without flip-flops)

I posted all this, because yesterday I found similar artifacts along the history of computing:
The article published in Scientific American the December of 1964:

Fluid logic devices, all based in the Coanda effect: 

And the conference at MIT:  
Referred by:  Fluidic computing at Bowles Fluidics:

Coding and computation in microfluidics.

And the conference from Manu Prakash,

The manu Prakash Thesis: (About "microfluidic bubble logic"), and inside this beautiful Truth table about logic gates and its equivalents in transistors, valves, electrical devices, and fluidics:

Some examples of projected fluidic devices:
(from Prakash thesis)
 Integrated fluidic logic gates with a schematic integrated control circuit 

The main patents about fluidics, come from the sixties:
(from wikipedia)

And schema about Coanda effect from Popular Science (Jun 1967 Pag 118) : 

And the:  Fluidics: Basic components and applications 
By: James W. Joyce  (1977; Unclassified: 1983)

And from the conference:
APPLIED HYDRAULICS AND PNEUMATICS U5MEA23 Prepared by Mr. Jayavelu.S & Mr. Shri Harish Assistant Professor, Mechanical.

I would like to see these companions of my program, running.

Anyway, everybody can see them inside the Bowles products:

And inside of the Theranos patented devices: (Lab-on-a-chip)

More serious and basic information: Introduction to fluid Mechanics:  

Follow: Reflections about all this at:

Wednesday, May 11, 2016

Dancing numbers: (Math Circus)

Dancing numbers: Numbers Circus: Modulo choreography.
( And:  Circus for to tame numbers, too )

After the post dedicated to dancing sort algorithms,  I think it's time to show a program made and published in 2004, which it could be useful in teaching elementary mathematics.

Is the "Dancing numbers

Originally made for , it never has been published. Finally I posted it on my page so do not be missed for the moment.

The program allows you to manipulate a lot of integers (up to 2000) with some simple rules: decide the number of columns that are to line up neatly from lowest to highest.
(Also possible to arrange smaller amounts of numbers)

The program allows for reflection on the divisibility of numbers and remainders:

It is also advisable to use the mode 9 columns, that shows the rule of divisibility for 9.
(The sum of all members of any number equals the heading number of the column)

And all the rules explained in
(related to addition, subtraction, multiplication and division (sometimes), and congruence).

Here is a sample of how the program works:

You can use the application here:

I hope its use will be useful to teach elementary mathematics.

Sunday, May 8, 2016

Noting mathematics education in the world, from the statistics page of my Android apps

This is just a small observation, based on my own stats:
As the numbers that I show are not too high, observation may not have enough value.

Typically, the math apps downloads have a proportion of users fairly well distributed among all countries. However, there is always a predominance of the US downloads:

Example graph of a usual app of active users statistics:

(humble numbers related to a calculator)

In my  Google Play page, there is one of the oldest applications that I've done, devoted to linear algebra and the  Gauss-Jordan elimination as a method of solving two equations with two unknowns.

For the application to be a little more attractive, I called it "Adding apples and oranges", referring to an equation are getting really different variables to give a result.

The proportion of current statistics of this application are quite different from other applications. There is a predominance of US downloads:

(humble numbers related to a Apples and oranges app)

While this difference so marked, it makes me think:
It could be that the education authorities of the US had greater knowledge of applied mathematics than education authorities of other countries?

Knowledge of the intellectual basis of the information revolution which we live has influenced the educational guidance of the US?
Or is the result of many parents with deep and old computer knowledge?

What is it that justifies this big difference?

I've searched Common Core related items with the elimination of Gauss-Jordan:
Here are some examples about the related items:


I can not draw a conclusion. Just leave the data in case anyone is able to solve these questions.