Cults

# Unit Fractions, Math Models

by Cults

Last crawled date: 4 years, 10 months ago

Unit fractions (1/N, for an natural number N) are interesting ideas in mathematics, dating all the way back to the ancient Egyptians. There are numerous ways to write a rational number as the sum of unit fractions. This is an an entry-level design project, allowing students to use their designs to play with basic ideas behind fractions. Among the files, 1 = 1/2 + 1/3 + 1/6, 1= 1/2 + 1/4 + 1/6 + 1/12, (1 = 1/2 + 1/3 + 1/10 + 1/15), (1 = 1/2 + 1/4 + 1/10 + 1/12 + 1/15), and 1 = 1/3 + 1/4 + 1/6 + 1/10 + 1/12 + 1/15. Of course, there are other ways to explore these ideas such as fraction bars and even 3D models (see Liu Hui's cube dissection).

Other combinations are possible but are physically less interesting:

1 = 1/2 + 1/3 + 1/8 + 1/24

1 = 1/2 + 1/3 + 1/9 + 1/18

1 = 1/2 + 1/4 + 1/5 + 1/20

1 = 1/2 + 1/5 + 1/6 + 1/8 + 1/120

1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/30

1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/20

1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/20

1 = 1/3 + 1/4 + 1/5 + 1/8 + 1/20 + 1/24

1 = 1/3 + 1/4 + 1/5 + 1/9 + 1/10 + 1/180

1 = 1/3 + 1/4 + 1/5 + 1/9 + 1/18 + 1/20

1 = 1/3 + 1/4 + 1/5 + 1/10 + 1/12 + 1/30

1 = 1/3 + 1/4 + 1/6 + 1/7 + 1/14 + 1/28

1 = 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24

1 = 1/3 + 1/4 + 1/6 + 1/9 + 1/12 + 1/18

References

http://mathworld.wolfram.com/EgyptianFraction.html

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html

Other combinations are possible but are physically less interesting:

1 = 1/2 + 1/3 + 1/8 + 1/24

1 = 1/2 + 1/3 + 1/9 + 1/18

1 = 1/2 + 1/4 + 1/5 + 1/20

1 = 1/2 + 1/5 + 1/6 + 1/8 + 1/120

1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/30

1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/20

1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/20

1 = 1/3 + 1/4 + 1/5 + 1/8 + 1/20 + 1/24

1 = 1/3 + 1/4 + 1/5 + 1/9 + 1/10 + 1/180

1 = 1/3 + 1/4 + 1/5 + 1/9 + 1/18 + 1/20

1 = 1/3 + 1/4 + 1/5 + 1/10 + 1/12 + 1/30

1 = 1/3 + 1/4 + 1/6 + 1/7 + 1/14 + 1/28

1 = 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24

1 = 1/3 + 1/4 + 1/6 + 1/9 + 1/12 + 1/18

References

http://mathworld.wolfram.com/EgyptianFraction.html

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html

## Similar models

thingiverse

free

### Unit Fractions, Math Models by lgbu

...ces
http://mathworld.wolfram.com/egyptianfraction.html
http://www.maths.surrey.ac.uk/hosted-sites/r.knott/fractions/egyptian.html

3dwarehouse

free

### Octagon Lamp

... lamp
3dwarehouse
#1 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #2 #20 #21 #22 #23 #24 #25 #26 #27 #28 #29 #3 #30 #4 #5 #6 #7 #8 #9

3dwarehouse

free

### Lumber Wood Set in Various to Scale (from Nominal to Actual ) Sizes

... 4 x 10 ….. #24= 2 x 4 x 8 #25= 2 x 3 x 12 .. #26= 2 x 3 x 10 .. #27= 2 x 3 x 8 #28= 2 x 2 x 12….#29= 2 x 2 x 10…. #30= 2 x 2 x 8

thingiverse

free

### BernieNet 1 by Fredbartels

...-7 64
12-4 130.5
12-6 111
13-7 95
13-8 91
13-6 116
14-6 103.5
14-8 96
14-5 99
15-5 94
15-8 94.5
15-9 120
16-7 113
16-8 89
16-9 78

thingiverse

free

### Maze on a Pumpkin by gigl

...n.
you can insert a 5mm diameter glass bad which to make your way through the maze ...
video is here:https://youtu.be/plxx-_zjzhw

thingiverse

free

### Sequence of Cubic Numbers and Multiplication Table by lgbu

...-2, n-1, n, n-1, n-2, ..., 3, 2, 1) = n x n^2.
of course, there are other ways to play with the multiplication table. have fun!

cults

free

### Triangular and Tetrahedral Numers

...hematical induction; they are as interesting as the visual structures. to print, please use raft for better adhesion to the bed.

thingiverse

free

### Fraction circle 1/2, 1/3, 1/4, 1/6, 1/8, 1/10, 1/12 by tfloveless

... 1/6, 1/8, 1/10, and 1/12 sized wedges as well as a circular base for them to fit onto. there are no labels on any of the pieces.

3dwarehouse

free

### really long hallway or is it

...really long hallway or is it
3dwarehouse
#1 #10 #11 #12 #13 #14 #15 #2 #3 #4 #5 #6 #7 #8 #9 #comfusing #hall #hallway #illusion

thingiverse

free

### Triangular and Tetrahedral Numers by lgbu

...hematical induction; they are as interesting as the visual structures. to print, please use raft for better adhesion to the bed.

## Fractions

turbosquid

free

### Fractional Distillation Tower

...andard mental-ray renderer and shaders.<br><br>nice clean mesh by professional 3d designer.<br><br>enjoy!

turbosquid

free

### Fountain pen

...instrument from the collection, divine. model is called ,

**fractions**...turbosquid

free

### Fountain pen

...instrument from the collection, divine. model is called ,

**fractions**in dark...turbosquid

$34

### Fire Extinguisher

...fire extinguisher
turbosquid
a single texture of 2048x2048<br><br>units are feet with fractional inches

turbosquid

free

### Moonshine Still

...lly correct and molded after commercially available parts. this model is a replica of a functioning compound fractionating still.

turbosquid

free

### Pizza Oven

...for body(1024x1024) and one for the front panel and patterns(2048x2048).<br><br>units are feet with fractional inches

turbosquid

free

### Fountain pen

...instrument from the collection, divine. model is called ,

**fractions**. <br>white gold finish.<br>all items in the render are...turbosquid

free

### AT_fractionating_column

...rvation, ... see the 'purchasing_the_models' link at appropedia's at_cad_team for additional information on the model

turbosquid

$55

### Jack Hammer

...plied 1024x1024 resolution<br><br>renderer used is iray<br><br>units used are feet with fractional inches

turbosquid

$6

### AGM-65 Maverick missile

...missile<br>very high quality<br><br>comparable to other agm-65 missile models at

**fractions**of the...## Math

turbosquid

free

### Maths board

...maths board
turbosquid
maths board

3ddd

$1

### Calligaris, Math

... calligaris , math
calligaris, math, журнальный столик

3d_export

$5

### Maths chalk board 3D Model

...maths chalk board 3d model
3dexport
maths keyboard
maths chalk board 3d model shadowlight123 86223 3dexport

turbosquid

$17

### Rotring Math Compass

... available on turbo squid, the world's leading provider of digital 3d models for visualization, films, television, and games.

3ddd

$1

### Потолочный светильник Math Ring

...ьник math ring
3ddd
kevin reilly , cosmorelax
диаметр (см): 83
количество ламп (шт.): 20

turbosquid

$7

### Math Object 0054

...t;-- obj ready for subdivision with any catmull-clark style algorithm.<br>-- export as subdivided geometry for 3d printing.

turbosquid

free

### Math Object 0055

...t;-- obj ready for subdivision with any catmull-clark style algorithm.<br>-- export as subdivided geometry for 3d printing.

turbosquid

free

### Math Object 0056

...e with 3dsmax 2017 or higher. <br>-- dimensions: x = 34.16mm, y= 9.059mm, z= 34.16mm <br>-- minimum thickness: 1.99mm

turbosquid

free

### Math Object 0093

...lt;br><br>object dimensions for 3d printing:<br><br>x = 45.62 mm<br>y = 45.62 mm<br>z = 45.62 mm

turbosquid

free

### Math Object 0068

...nsubdiv modifier in the stack. <br>-- dimensions: x = 22.92mm, y= 5.667mm, z= 23.62mm <br>-- minimum thickness: 1.0mm

## Unit

archibase_planet

free

### Unit

...unit
archibase planet
desk board
entertainment unit 02 - 3d model (*.gsm+*.3ds) for interior 3d visualization.

turbosquid

free

### Wall unit

...wall unit
turbosquid
wall unit tv unit

turbosquid

free

### Wall unit

...wall unit
turbosquid
tv unit wall unit

turbosquid

$7

### Shower Unit

...shower unit
turbosquid
a highly detailed shower unit with attached head unit.

3d_export

$15

### control unit

...control unit
3dexport
control unit

3ddd

$1

### bathroom unit

...bathroom unit
3ddd
bathroom unit

turbosquid

free

### decoriton unite

...decoriton unite
turbosquid
decoration unite

turbosquid

free

### tv unit

...tv unit
turbosquid
tv unit

turbosquid

free

### TV Units

...tv units
turbosquid
tv units

turbosquid

free

### Unit TV

...unit tv
turbosquid
unit tv