Nummòlt - construction toys - Mathematical engine mill.

Math Cats are welcome here. Link to Math Cats.

www.nummolt.com

Math manipulatives & construction toys

Visit our page: OBBL math toys & games
Adding apples and oranges (pears, lemons...), Egyptian fractions, How much pizza? ...

Math toys.

Math tools.

View and touch mathematics.

Primes as the basic building blocks of numbers.

Teaching resources: mathematics and physics.

Mill of numbers - Mathematical engine mill: - nummolt blog

Double Struck Capital: - Double Struck Capital

Nummolt apps: - nummolt apps - Google Play

Explore Tessellations (Android)

Explore Tessellations

Explore Tessellations
The 28 ways to tile a flat surface with asymmetric tiles by Heinrich Heesch
To understand Escher Tessellations and create new monotiles
An easy-to-use tool to create, design, save and load tessellations from the 28 heesch prebuilt tile types

Explore Tessellations: youtube: Youtube playlist

Examples of 28 Heesch tessellations made with Explore Tessellations:
Heesch 1: TTTT Unicorn
Heesch 2: TTTTTT Dog
Heesch 3: CCC Cat
Heesch 4: CCCC Wolf
Heesch 5: TCTC Crab
Heesch 6: TCTCC Swimmer
Heesch 7: TCCTCC Elephants
Heesch 8: C3C3C3C3 Turtle
Heesch 9: C3C3C3C3C3C3 Fox
Heesch 10: CC3C3 Fish
Heesch 11: CC6C6 Cat
Heesch 12: C3C3C6C6 Elephant
Heesch 13: CC3C3C6C6 Dancing
Heesch 14: CC4C4 Mermaid
Heesch 15: C4C4C4C4 Puzzle piece
Heesch 16: CC4C4C4C4 Dog
Heesch 17: G1G1G2G2 Goose
Heesch 18: TG1G1TG2G2 Hexagon Cat
Heesch 19: TGTG Bird
Heesch 20: TG1G2TG2G1 Parrot
Heesch 21: CGG Firebird
Heesch 22: CCGG Fish
Heesch 23: TCTGG Rat
Heesch 24: TCCTGG Lobster
Heesch 25: CGCG Lizard
Heesch 26: G1G2G1G2 Curvy Bird
Heesch 27: CG1G2G1G2 Dog
Heesch 28: CG1CG2G1G2 Birds

Proportion & Slope (Android)

Proportion & Slope

Proportion and Slope
App that attempts to graphically show what is routinely done with cross multiplication.

Shows the slope, the ratio, the proportion between two numbers, and allows applying that proportion to other numbers, whether they are greater or less than the initial one.
Graphically the proportion is fixed with the red bars.
The blue dot slides down the slope fixed by the proportion.

Videos: Proportion and Slope

Visual Algebra (Android)

Visual Algebra

Visual Algebra
Help tool to solve algebra problems graphically
linear, quadratic, cubic and more.....
Help files to learn how to solve problems graphically with Visual Algebra: 14 examples: trains, water tank, painters, overlapping clock hands, two ages, perimetral path added to a garden, square growing, rule of 3, split trapezoid...

Videos:
Video 1: Trains Crossing
Video 2: Trains Chasing
Video 3: Water Tank
Video 4: Painters
Video 5: Clock Hands Overlapping
Video 6: Two Ages
Video 7: Garden
Video 8: Square Growing
Video 9: Consecutive Numbers
Video 10: Square Box
Video 11: Cuboid
Video 12: Direct Rule of 3
Video 13: Inverse Rule of 3
Video 14: Trapezoid (old sumerian puzzle)

Measure Fractions (Android)

Measure Fractions

Measure Fractions
Measuring proper fractions and improper fractions

Measure Fractions displays a mesh of unit squares that can be divided into different partitions both horizontally and vertically, and fill the mesh with colors to form different fractions.
The app measures the fraction that corresponds to each color, and adds everything that can be seen on the board on the line shown at the top.
The app is useful for practicing addition, subtraction, division and multiplication of fractions.

Videos: Measure Fractions: The 4 Operations

Euclidean Prime Rectangle (Android)

Euclidean Prime Rectangle

Euclidean Prime Rectangle
Interactive rectangle

The area of a rectangle is the result of product of its sides.
Shows integer points of rectangles with same area

Videos: Euclidean Prime Rectangle

Rectangle of constant area (Android)

Rectangle of constant area

Rectangle of constant area
Geometry help to understand division of fractions

The area of a rectangle is the result of product of its sides..
The division of the area of a rectangle by one of its sides is the length of the other side.
Every rectangle of constant area is limited by its hyperbola
Understanding the division of fractions, and for the fruitless search for the square root of 2, 3, 5 etc. in rational numbers..

Videos: Rectangle of constant area

Conic Anamorphism Cameras (Android)

Conic Anamorphism

Conic Anamorphism
Build a conic anamorphism with the Conic Anamorphism Camera

Get the original image (from anamorphism) with the Virtual Cone Mirror Camera.
Save original and anamorphic images to the App/Files/Pictures folder
Get anamorphisms from folder images with Conic Anamorphism Camera
Recover original images from anamorphisms of the folder with the Virtual Cone Mirror Camera.

Videos: Conic Anamorphism

Geoboard (Android)

Geoboard

Geoboard
Geoboard:

Buttons:
0=0 Insert new rubber band.
T Erase rubber band.
Col Change rubber band color.
A Calculate area.

Practice:
Calculate area contained inside the rubber band (only in square mesh).
Convex, concave polygons, positive or negative areas.
Videos: Geoboard

Voronoi Soccer / Football (Android)

Voronoi Soccer / Football

Voronoi Soccer / Football
Soccer game showing the Voronoi Diagram.

The Voronoi diagram is the partition of a space in the regions closest to different points.
The closest regions here are those that belong to each of the players.
Voronoi diagrams are constructed from the triangulation of Delaunay.
In this game you can modify the positions of the players just by touching the screen.
In this game you can change the alignment of players from a long list of historical formations
The players decide the best pass from the analysis of the edges of the Delaunay triangles.
And when they advance with the ball, they usually send it to the more advanced point of their Voronoi region.
Except when they are close to the opposing goal: Then they try to shoot the ball towards the center.
When they advance with the ball they only do so with the idea of reaching it again after having kicked it..
Videos: Voronoi Soccer / Football

Euler & Hamilton Path (Android)

Euler - Hamilton Path

Euler - Hamilton Path
Find Euler Path or Hamilton Path in a Graph.

Build edit and save new graphs:
Graph Theory.
Avoid bridges in Euler Path.
Find the shortest Hamilton Path.

From Idea Suggested by: Guido Ramellini (MMACA).
Videos: Euler - Hamilton Path

Reading Fractions (Android)

Reading Fractions

Reading Fractions
Read fractions - Reading fractions.

Basic tool for to experiment with fractions:
The app lets you view the fractions represented in the form of overlapping circles and bars.
The two graphs are interactive. They can be changed by dragging on the screen.
Graphically, fractions are always shown in simplified form.
There are two spinners to select fractions: one for the numerator and one for the denominator.
At the right there are two lock buttons:
The top button locks the numerator when the graph is modified.
The lower button locks the denominator when the graph is modified.
Additionally fractions are shown in written words, mixed fractions (if needed) as a percentage and as a decimal number with dot.
Videos: Reading Fractions

Equivalent Fractions (Android)

Equivalent Fractions

Equivalent Fractions
Create equivalent fractions by dividing and shading squares or circles, and match each fraction to its location on the number line.

Check your work, and use the table feature to capture results and look for patterns.
Got a particular value for which you’d like to make equivalent fractions? Use “Build Your Own” mode.
When the time comes to harvest dandelions, the plant is plucked from the ground.
Two options for teachers:
"Settings (automatic mode)": To adjust the difficulty of the problems generated by the app.
"List sessions history": To see the last 50 right results obtained with the app.
Originally something similar to this app was developed by Illuminations, a project of the National Council of Teachers of Mathematics, and erased from the Google Play list some years ago.

This is a rebuilt version from scratch dedicated to the Math Forum staff all of whom have recently lost their jobs at NCTM.
Videos: Equivalent Fractions

Proper Fractions(Android)

Proper Fractions

Proper Fractions
Equivalent fractions (Using Proper Fractions):

Compare proper fractions in a circle with proper fractions in a square.
Increase or decrease the number of sections with 'pinch zoom'.
Open-ended explorations or guided options. (Select at: top bar)
(Or play with the Ahmes 2/n table of the RMP, like in the main video of the app)
(Or play with the table shown in the Akhmim Papyrus)
(Suggested by: Milo Gardner, Cryptanalyst)

Videos: Proper Fractions: Akhmin n/17 Table

Math Garden (Android)

Math Garden

Math Garden
In this app, the natural numbers are represented as vegetables (plants):.

Plants similar to: Dandelions, (from French: 'dent-de-lion').
They should be planted. And then grow the plant corresponding to the seed (and the number chosen).
When the time comes to harvest dandelions, the plant is plucked from the ground.
Then the seeds that it has generated are released.
And the seeds return to heaven.
If two unseeded seeds overlap, they add up.
If two seeds are planted, the plants multiply.
The plants are structured in branches, forking in function of the prime numbers that compose the factorization of the number.
The program has 30 furrows one behind the other to be able to plant.
Videos: Pythagorean Garden

Fractions Balance (Android)

Fractions Balance

Fractions Balance
Pan balance: Fractions.

Balance fractions. (Fractions division).
Balance a fractions balance scale, multiplying fractions by prime numbers. (division of fractions)
Live fulcrum and balance scale.
When the time comes to harvest dandelions, the plant is plucked from the ground.
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.
This imbalance, when the ratio is proportional to the ratio of content of the dishes, is also the result of the division.
(This app is the logical continuation of the work done in "Mathcats balance" of MATHCATS).
Videos: Fractions Balance

Fractions Scroll (Gravity Lever) (Android)

Fractions Scroll

Fractions Scroll Gravity Lever
Fractions Scroll Gravity Lever.

Explore Fractions, Scrolling Irreducible Fractions.
Allows to use the Device's Gravity Sensors.
Scroll Horizontal: Swipe: From (1/n to n/1)
Scroll Vertical: Swipe: n from 4 to 80 (Maximum recommended 50)
Tool to explore sorted fractions.

Show fraction, Pie shape, squared Graph, Slope, Decimal with decimal mark.
The Standalone Fulcrum of the MathCats Balance.
FREE VERSION:
There's a free version without gravity sensor (same author)
Fractions Scroll
Videos: Fractions Scroll Video

Euclidean Algorithm GCD (Android)

Euclidean Algorithm GCD

Euclidean Algorithm GCD
Animated Euclidean Algorithm.

Greatest Common Divisor.
Useful to reduce fractions.
GCD, also known as the greatest common factor (gcf), highest common factor (hcf), greatest common measure (gcm), or highest common divisor.
Then the seeds that it has generated are released.
Dynamic and geometric representation of the algorithm.

The Euclidean algorithm is one of the oldest algorithms in common use.
It appears in Euclid's Elements (c. 300 BC), specifically in Book 7 (Propositions 1–2) and Book 10 (Propositions 2–3).
Centuries later, Euclid's algorithm was discovered independently both in India and in China, primarily to solve Diophantine equations that arose in astronomy and making accurate calendars.
Acknowledgements: Joan Jareño (Creamat) (Addition of lcm).
Videos: Euclidean Algorithm GCD

Touch Integers ℤ (+ - × ÷) (Android)

Touch Integers ℤ (+ - × ÷)

Touch Integers ℤ (+ - × ÷)
Add, subtract multiply and divide integers in a visual and interactive way.

Is very easy add and substract graphically. One can regroup the tokens of each order, regroup, carry or borrow tokens, and you can obtain the result.
But not so easy to practice multiplication or division in this visual and interactive way.
I tried to think as a research physicist of the atom:
I looked the inside of the numbers:
Inside the numbers there are the components of the number: The prime factors.
To multiplicate two integers you must regroup the components of the two numbers.
To divide a integer, you must separate the components.
The program only works with integers. adds, subtract, multiplies and divides (but only exact division) using the prime factors of the numbers.
The behavior of places and tokens of this app describes the behavior of the numbers in the ℤ set.
Videos: Touch Integers ℤ (+ - × ÷)

Touch decimals Place value ± (Android)

Touch decimals Place value ±

Touch Decimals Online

Touch decimals Place value ±
Interactive double place value chart with positive and negative tokens.
Wireless abacus.
Designed to:
- Show and experience the addition and addition with carry.
- Show and experience the subtraction and subtraction with borrowing.
- Zero as "nothing" in a place value place, or as an undetermined number of negative-positive pairs of particles with sign.
The behavior of places and tokens of this app describes the behavior of the numbers in the decimal system.
Blog: Post: Touch decimals Place value ± Chapter 1: References:
Videos: Touch decimals (PlayList)
Touch decimals (promotional video v: 1.1.x)
Touch decimals: Borrowing (pre-release video)
Touch decimals: Carry (pre-release video)
Touch decimals: Transition (pre-release video)

Touch Math apps: (Android)

Touch Natural Numbers

Touch Natural Numbers:
Small laboratory of Natural Numbers:
The Prime numbers are like the building blocks of the numbers.
With this app you can:
Analyze the factors of a Composite number.
Build a Composite number from its factors. (multiplication and division of Natural Numbers)
Localize or select a number in the Ulam Spiral.
Verify all the possible products between Primes in a composite number with the Parabolic Sieve.
Analyze or build a number with the Place Value activity (Addition or Subtraction)
Understand the Modulo of a number.
Introducing the polygonal numbers.
Know the numbers as the sum of two prime numbers or as the sum of three prime numbers.
Touch Natural Numbers (video)

Touch Fraction

Touch Fraction:
Construction of the rational numbers.
Interactive fraction app.
Select equivalent fractions with the rational representation diagram.
The program is useful to understand:
fractions, coordinate geometry, rational numbers, cartesian plane, slope,
and the equivalent classes of pairs of integers.
video playlist

Touch Pythagoras

Touch Pythagoras:
Touch Pythagoras
Interactive Pythagoras Theorem app.
video playlist

OBBL Math Toys Android apps:

How much pizza

Adding apples and oranges

$old egyptian fractions$
Old egyptian fractions

Ninedigits workshop

Apples and oranges 1 decimal

$Reading fractions$
Reading fractions

Time Calculator

Whole Calculator

Calculadora Natural

$Adding unit fractions$
Adding unit fractions

$adding unit fractions +$
Adding unit fractions

Nummolt modulo applet.

Nummolt Modulo applet (May 2012: v2.02) (Work in progress).
Base ten blocks, addition, subtraction, Polygonal numbers, Modular arithmetics. [Java applet]
Video help files at: www.nummolt.com/modulo/help/index.html.

nummòlt.
From 7 years

Base 10 blocks manipulative: Integers are transformed into small blocks. That can be manipulated to solve elementary operations. Is useful to teach about numbers, place value, and elementary operations.
Matters: borrowing in subtraction, adding positive and negative numbers, multiplication by negative numbers....

160Kb. Win16 Windows9X nummolt.zip

Online Help:

Done in 1998 Release 3 Developing time: 1995/6/7 (C++)
Video Help: -- + -- * /? () -(x) +x-x +-?
Video Help: Playing: Quadrillion Signed parenthesis

obbl.
For everybody. (Elementary )

Construction toybox: Building blocks: Flat blocks. With gravitation. Beam blocks adhere among them. Thumbtacks are fixed blocks.

JavaScript (cellular automata)

Done in 2000 - 2001.

Activity: Adding integers: 1+2+....+n.

Collaboration:
with MathCats in obbl.

Playing with OBBL:

Little archaeologist...

Math
Water
Table.
(All ages).

Area workshop. Container blocks. To explain area and division.
It converts numbers in area units.
To measure area, filling figures. Didactic tool, and also a toy.
(Former Obbliq).

JavaScript + html5
(cellular automata)

August 2001-Feb 2005.
Feb 2013:
MWT Math Water Table v.1.0.0: MWT video help (youtube)

Old obbliq Help:
Obbliq and division #1: #2: Obbliq and Piaget's volume conservation
old obbliq video help Index:
Vol 3*2=2*3 3/0.5 PI

obblog 2.
From 15 years.

Logic construction toybox. Logic blocks. To explain binary logic, and learn about truth tables. It allows to keep the work. Binary logic simulator. Binary calculator

JavaScript + html5
(cellular automata)

Done in 2001 (Cellular automata.).
Updated: 2013
Help:
Obblog2 YouTube Playlist
Old Help:
Truth Tables videos: index
Binary counter
Binary countdown

Balance simulated: to weigh electrons, neutrons, atoms, virus, bacteria, ants, flies, eggs, thin cats, jumping cats, fat cats, donkeys, elephants, dinosaurs, houses, skyscrapers, pyramids, comets, moons, planets, stars and galaxies

MathCats Balance.
All ages.
MathCats Balance ANDROID.

Balance: To weigh a wide range of objects: from electrons to galaxies. Cats included. To play with division, fractions, multiplications, rational numbers, huge numbers and tiny numbers.

JavaScript

Done in 2003.
Help:
Balance Help
Collaboration:
Math Cats - Nummòlt

cinemice
Cinemice projector: V.01

Cinemice Projector: Format compatible with Cine Nic Projectors (Super Nic format). Toys and Cinema. Films posted with permission. (Museu del Cinema de Girona).

JavaScript/Java Navigator / Explorer

Done 2004-2012:
Museu del Cinema: www.museudelcinema.cat
Standalone cinemice
Offline version:
Cinemice main page
From Cinemice to reality:
From Cinemice to Cine-NIC

Cinemice Android
Boni's Cinemice site:
Boni's Cinemice

Cinemice apps: (Android)

Camera Patchwork

Camera Patchwork:
The application allows 360 degree views.
The program builds the image using a projection of the sphere similar to Mollweide.
The images are constructed from 300 small images.
The camera takes a picture when it detects a new spin 8 degrees in either direction.
Move the camera slowly.
We recommend vertical sweeps, moving to the right or the left.
Free app
Camera Patchwork Gallery: