This week (after a month of work) we started a new project : "Double Struck Capital ".
And for the first time we can post about it on this blog.
The first visible result of this project is the calculator of natural numbers: "Whole Calculator"
It works in the set of the Natural Numbers (ℕ0 in the mathematical text books)
'ℕ' is the character named 'Double-struck Capital N'
Our new calculator has the particularity to work with arbitrarily large numbers (up to centillion). And it can show the numbers written in words.
One purpose of this program is to support the teaching of reading whole numbers, and to be able to read and operate with numbers and huge numbers too.
And has another intention:
In the attempt to understand the numbers and its elementary operators in a first stage of education, it is relatively easy to explain the sum , and multiplication.
But subtraction and division operations are another level :
Subtraction and division are operations whose result that is not restricted into the set of natural numbers:
Therefore, you can only partially explain those operations :
Subtraction, only when the result is always positive.
The division only when a provided that the dividend is a multiple of the divisor.
The Whole Calculator , tries to show this same state of bewilderment :
While it is capable of displaying numbers to barely imaginable figures (is able to show correct results in numbers and letters up to 10 ^ 303) however it is not able to operate with negative numbers, and if the divisions are not exact , the result has a remainder .
"Whole calculator " is a coherent and 'trustable' product . But, when results are not within the set of natural numbers , warns the user that the " this calculator of natural numbers is not able to give the correct result" , because it is outside the scope of the natural numbers, and recommends the use (and "download" from anywhere) a better calculator: integer calculator (ℤ) or rational (ℚ) as appropriate: As if the app were a damaged or a incomplete product.
We want to show that the "whole calculator" is a damaged product, by fault of the Natural Numbers.
In turn, all this can be seen as a joke by program users .
But in "Double Struck Capital - nummòlt " we think it is a way to teach the numbers from the beginning:
Understand that in a first step , we learn to live with the numbers used to count and to list . But when we operate with them, and as we operate, we have not enough with these numbers (natural numbers) and we need to expand the range of numbers to use, to meet the needs that appear when we afford the subtraction and the division.
At the time of making this app, we had to deal with the construction of the natural numbers from zero :Internally, the program works with the natural numbers as a String variable , so that the numbers do not remain limited to the small dimensions of the variables of type ' int ' or ' long' .This has forced the developer to implement the algorithm of addition, subtraction, multiplication and division from text strings.
And we have faced the same problem as has a child when learns to add, subtract, multiply and divide.
Recovering these skills almost lost in time for us, we has discovered that we never fully understood the algorithms of subtraction, or multiplication or division.
- We have not clear enough the mechanism of "I carry" in the addition or "borrowing" in subtraction .
- We don't know subtract if the result will not be positive .
- We do not understand what we do when we multiply numbers: ( The needed zeros are obviated in the mechanism we were taught in school)
- We do not understand almost nothing of the procedure that we follow when we divide .
In the development of this program, we felt like little kids , having to learn the most basic things.
And at the same time , we felt like kids happy when it was finished.
We expect that when the program will be downloaded, the users will can get to enjoy it as we have enjoyed making it .
The program can be downloaded at:
(There's only the Android App, no version in other operative systems)
Whole Calculator Youtube:
How looks a Centillion?:
There's also a paid version in Castilian ( Spanish ) spelling the natural numbers from 1 to the "Centillón" (1^600) working with the Long Scale:
Video of the Update (Version 1.0.4):
Video of the Update (version 1.0.7) added Catalan:
Video about Factorials: From 2! to 50!:
Thanks for the help:
Wendy Petti (mathcats.com)
Joan Jareño (CREAMAT)
Maurici Carbó (nummolt webmaster)