Modulo Art -computer Based Design 4b631g
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HOME
ABOUT MA21C
NEWS
IMAGES
FEATURES
MULTIMEDIA
A comput erbased design
MODUL AR: st Modulo Art in the 21 Century Twentyfircent Presentation
Modulo - Addition Modulo - Subtraction Modulo - Multiplication Modular Arithmetic Sample
LIVIN G. REJUSO Proponent MODULO ART: Computer- Based Design
ADVANTAGES 1. Cost effective. No need for student to buy materials to create design. 2. Flexible and comfortable. Student can only use the mouse in creating design.
MODULO ART: Computer- Based Design By: Livin G. Rejuso
ADVANTAGES 3. Modification of the art/ design. In computer there are available tools like auto shapes, editing tools, draw tools, dimension tools, fill color, line color and many more. Using the tools, all designs can be accurate in dimension, allow quick easy editing, adding realistic details, provide simple alignment. Combining these tools you have endless possibilities.
MODULO ART: Computer- Based Design By: Livin G. Rejuso
ADVANTAGES 4. Tireless- lay out the design conveniently. 5. Controlled-can draw accurately. 6. Product quality
MODULO ART: Computer- Based Design By: Livin G. Rejuso
OBJECTIVES: Use modular operations to create pattern/s to form modulo art Use computer in deg modulo art
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Mathematics is also a study of patterns . One of the ways in which we use number patterns is in the creation of unique and artistically pleasing designs. This design from number pattern in Modular Arithmetic formed Modulo Art.
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modular Arithmetic
modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss MODULO ART: Computer- Based Design By: Livin G. Rejuso
9
1 1 1 0
1 2
1 2 3 4
8 7
6
5
What is the time if you add 5 hours to 11 o’clock?
MODULO ART: Computer- Based Design By: Livin G. Rejuso
9
1 1 1 0
1 2
1 2 3 4
8 7
6
5
What is the time if you add 12 hours to 12 o’clock?
MODULO ART: Computer- Based Design By: Livin G. Rejuso
9
1 1 1 0
1 2
1 2 3 4
8 7
6
5
9 o’clock + 9 hours? MODULO ART: Computer- Based Design By: Livin G. Rejuso
1 8 2 4 0 1 7 3 1
1 5 9 2 6 1 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 3
1 2
Modulo= Remainder or Residue
Modulo 4
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Activity Complete the table using Modular Arithmetic . Addition Subtraction Multiplication
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Activity Complete the table using Modular Arithmetic
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modular Arithmetic Modulo 4- Addition 0
1
2
3
1
2
3
0
2
3
0
1
3
0
1
2 MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modular Arithmetic Modulo 4Subtraction 0 1 2 3 1
0
3
2
2
1
0
3
3
2
1
0 MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modular Arithmetic 0
Modulo 4Multiplication
1
2
3
1
1
2
3
2
2
0
2
3
3
2
1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modulo 4- Addition If we make
0
1
2
3
as our legend…… MODULO ART: Computer- Based Design By: Livin G. Rejuso
If we substitute each legend to our pattern, what happen?
0
1
2
3
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modular Arithmetic Modulo 4Subtraction 0 1 2 3 1
0
3
2
2
1
0
3
3
2
1
0 MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modulo 4Subtraction
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modular Arithmetic 0
Modulo 4Multiplication
1
2
3
1
1
2
3
2
2
0
2
3
3
2
1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
2
3
MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
Addition P A T T E R N
Multiplicatio n
Subtraction
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Addition
Subtraction
Multiplicatio n
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Addition
Subtraction
Multiplicatio n
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Addition
Subtraction
Multiplicatio n
MODULO ART: Computer- Based Design By: Livin G. Rejuso
5 TYPES OF MODULO ART 1. Grid /Latin square
MODULO ART: Computer- Based Design By: Livin G. Rejuso
2. Converging segment
MODULO ART: Computer- Based Design By: Livin G. Rejuso
3. Standard Kaleidoscope
MODULO ART: Computer- Based Design By: Livin G. Rejuso
4. Circular Kaleidoscope
MODULO ART: Computer- Based Design By: Livin G. Rejuso
5. Residue Kaleidoscope
MODULO ART: Computer- Based Design By: Livin G. Rejuso
1. Latin square
MODULO ART: Computer- Based Design By: Livin G. Rejuso
2. Converging segment/design
3. Standard Kaleidoscope
4. Circular Kaleidoscope
Modulo Art: Grid lines/ Latin Square design (Repeated, Reflected and Rotated) Modulo Art- Circular Kaleidoscope Design (Repeated, Reflected and Rotated) Modulo Art- Standard Kaleidoscope Design (Repeated, Reflected and Rotated) Modulo Art- Converging/Diverging Design (Repeated, Reflected and Rotated)
ABOUT MA21C
NEWS
IMAGES
FEATURES
MULTIMEDIA
A comput erbased design
MODUL AR: st Modulo Art in the 21 Century Twentyfircent Presentation
Modulo - Addition Modulo - Subtraction Modulo - Multiplication Modular Arithmetic Sample
LIVIN G. REJUSO Proponent MODULO ART: Computer- Based Design
ADVANTAGES 1. Cost effective. No need for student to buy materials to create design. 2. Flexible and comfortable. Student can only use the mouse in creating design.
MODULO ART: Computer- Based Design By: Livin G. Rejuso
ADVANTAGES 3. Modification of the art/ design. In computer there are available tools like auto shapes, editing tools, draw tools, dimension tools, fill color, line color and many more. Using the tools, all designs can be accurate in dimension, allow quick easy editing, adding realistic details, provide simple alignment. Combining these tools you have endless possibilities.
MODULO ART: Computer- Based Design By: Livin G. Rejuso
ADVANTAGES 4. Tireless- lay out the design conveniently. 5. Controlled-can draw accurately. 6. Product quality
MODULO ART: Computer- Based Design By: Livin G. Rejuso
OBJECTIVES: Use modular operations to create pattern/s to form modulo art Use computer in deg modulo art
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Mathematics is also a study of patterns . One of the ways in which we use number patterns is in the creation of unique and artistically pleasing designs. This design from number pattern in Modular Arithmetic formed Modulo Art.
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modular Arithmetic
modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss MODULO ART: Computer- Based Design By: Livin G. Rejuso
9
1 1 1 0
1 2
1 2 3 4
8 7
6
5
What is the time if you add 5 hours to 11 o’clock?
MODULO ART: Computer- Based Design By: Livin G. Rejuso
9
1 1 1 0
1 2
1 2 3 4
8 7
6
5
What is the time if you add 12 hours to 12 o’clock?
MODULO ART: Computer- Based Design By: Livin G. Rejuso
9
1 1 1 0
1 2
1 2 3 4
8 7
6
5
9 o’clock + 9 hours? MODULO ART: Computer- Based Design By: Livin G. Rejuso
1 8 2 4 0 1 7 3 1
1 5 9 2 6 1 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 3
1 2
Modulo= Remainder or Residue
Modulo 4
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Activity Complete the table using Modular Arithmetic . Addition Subtraction Multiplication
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Activity Complete the table using Modular Arithmetic
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modular Arithmetic Modulo 4- Addition 0
1
2
3
1
2
3
0
2
3
0
1
3
0
1
2 MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modular Arithmetic Modulo 4Subtraction 0 1 2 3 1
0
3
2
2
1
0
3
3
2
1
0 MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modular Arithmetic 0
Modulo 4Multiplication
1
2
3
1
1
2
3
2
2
0
2
3
3
2
1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modulo 4- Addition If we make
0
1
2
3
as our legend…… MODULO ART: Computer- Based Design By: Livin G. Rejuso
If we substitute each legend to our pattern, what happen?
0
1
2
3
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modular Arithmetic Modulo 4Subtraction 0 1 2 3 1
0
3
2
2
1
0
3
3
2
1
0 MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modulo 4Subtraction
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
S U B T R A C T I O N
0 1 2 3
1 0 1 2
2 3 0 1
3 2 3 0
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Modular Arithmetic 0
Modulo 4Multiplication
1
2
3
1
1
2
3
2
2
0
2
3
3
2
1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
2
3
MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
M U L T I P L I C A T I O N
0
1
0 1 2 3
1 1 2 3
2
2 2 0 2
3
3 3 2 1 MODULO ART: Computer- Based Design By: Livin G. Rejuso
Addition P A T T E R N
Multiplicatio n
Subtraction
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Addition
Subtraction
Multiplicatio n
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Addition
Subtraction
Multiplicatio n
MODULO ART: Computer- Based Design By: Livin G. Rejuso
Addition
Subtraction
Multiplicatio n
MODULO ART: Computer- Based Design By: Livin G. Rejuso
5 TYPES OF MODULO ART 1. Grid /Latin square
MODULO ART: Computer- Based Design By: Livin G. Rejuso
2. Converging segment
MODULO ART: Computer- Based Design By: Livin G. Rejuso
3. Standard Kaleidoscope
MODULO ART: Computer- Based Design By: Livin G. Rejuso
4. Circular Kaleidoscope
MODULO ART: Computer- Based Design By: Livin G. Rejuso
5. Residue Kaleidoscope
MODULO ART: Computer- Based Design By: Livin G. Rejuso
1. Latin square
MODULO ART: Computer- Based Design By: Livin G. Rejuso
2. Converging segment/design
3. Standard Kaleidoscope
4. Circular Kaleidoscope
Modulo Art: Grid lines/ Latin Square design (Repeated, Reflected and Rotated) Modulo Art- Circular Kaleidoscope Design (Repeated, Reflected and Rotated) Modulo Art- Standard Kaleidoscope Design (Repeated, Reflected and Rotated) Modulo Art- Converging/Diverging Design (Repeated, Reflected and Rotated)
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