Thingiverse
Pythagoras on Hinges, Dissection Models for the Pythagorean Theorem by lgbu
by Thingiverse
Last crawled date: 3 years ago
Pythagoras on Hinges, Dissection Models for the Pythagorean Theorem
There are numerous ways to prove the Pythagorean Theorem! And there are also many ways to make sense of the squares on the three sides of a right triangle using dissections. In the present design, I used a classic dissection, where the square on the longer leg is dissected into four congruent quadrilaterals and further hinged with the square on the short leg. Hence, we have a string of five (3D) shapes, which can be folded into the square (box) on the hypotenuse, or the two squares (boxes) on the two legs. The pictures speak for the transformation. Of course, the height of the model does not count with the Pythagorean Theorem. Nonetheless, since the pieces all have the same height in a specific model, the volumes of the three boxes (outer) also follow the Pythagorean Theorem.
To use the dissection model, one needs to print at least one set of the five-piece file, leaving the right triangle to the imagination. If so desired, one can use two copies of the five-piece file plus the corresponding right triangle. Of course, the five-piece structure also behaves like a puzzle—one square to/from two squares. Have fun!
Among the files
Five-piece structure in two sizes (25-50-hypotenuse, 40-100- hypotenuse)
Right triangle in two sizes (25-50-hypotenuse, 40-100- hypotenuse)
References
https://www.cut-the-knot.org/pythagoras/
https://www.cs.purdue.edu/homes/gnf/book.html
There are numerous ways to prove the Pythagorean Theorem! And there are also many ways to make sense of the squares on the three sides of a right triangle using dissections. In the present design, I used a classic dissection, where the square on the longer leg is dissected into four congruent quadrilaterals and further hinged with the square on the short leg. Hence, we have a string of five (3D) shapes, which can be folded into the square (box) on the hypotenuse, or the two squares (boxes) on the two legs. The pictures speak for the transformation. Of course, the height of the model does not count with the Pythagorean Theorem. Nonetheless, since the pieces all have the same height in a specific model, the volumes of the three boxes (outer) also follow the Pythagorean Theorem.
To use the dissection model, one needs to print at least one set of the five-piece file, leaving the right triangle to the imagination. If so desired, one can use two copies of the five-piece file plus the corresponding right triangle. Of course, the five-piece structure also behaves like a puzzle—one square to/from two squares. Have fun!
Among the files
Five-piece structure in two sizes (25-50-hypotenuse, 40-100- hypotenuse)
Right triangle in two sizes (25-50-hypotenuse, 40-100- hypotenuse)
References
https://www.cut-the-knot.org/pythagoras/
https://www.cs.purdue.edu/homes/gnf/book.html
Similar models
sketchfab
$15
Pythagorean Theorem
... in literature, plays, musicals, songs, stamps, and cartoons abound. - pythagorean theorem - buy royalty free 3d model by arloopa
thingiverse
free
Pythagorean Theorem on Hinges with Equilateral Triangles by lgbu
...fine! however, we don’t have to use squares. any similar 2d shapes constructed on the three sides of the...
cults
free
Key Chain, Pythagoras, Pythagorean Theorem
... visually proves the pythagorean theorem. it is easy to print. please try a higher resolution for a smooth appearance. have fun!
cults
free
Pythagoras, Pythagorean Theorem, 3D Models, 勾股定理, ピタゴラス定理
...the three 3d solids (or corresponding 2d shapes) are similar to each other, the volume of the solid on...
thingiverse
free
Pythagoras, Pythagorean Theorem, 3D Models, 勾股定理, ピタゴラス定理 by lgbu
...the three 3d solids (or corresponding 2d shapes) are similar to each other, the volume of the solid on...
3dwarehouse
free
pythagorean theorem
...pythagorean theorem
3dwarehouse
pythagoras in a triangle, geometry
thingiverse
free
Key Chain, Pythagoras, Pythagorean Theorem, 勾股定理, ピタゴラス定理 by lgbu
...ually proves the pythagorean theorem. it is easy to print. please try a higher resolution for a smooth appearance. have fun!
thingiverse
free
Pythagorean Puzzle by UMF3D
...thagorean theorem by using the pieces from 2 smaller sides to create the hypotenuse squared.
c. heckley & g. wright, may 2018
thingiverse
free
Pythagorean Theorem Ornaments by paulblankenbaker
...this allows the pieces to be converted into ornaments that can serve as annual reminder of the proof each year over the holidays.
thingiverse
free
Pythagorean Theorem by MaximusG
...two of the bases. the base file is ptb, standing for pythagorean theorem base. this is perfect to teach kids about this equation.
Pythagoras
turbosquid
$239
Pythagoras
...bosquid
royalty free 3d model pythagoras for download as stl on turbosquid: 3d models for games, architecture, videos. (1415673)
3d_sky
free
Pythagoras stoel
...pythagoras stoel
3dsky
http://www.gimmii.nl/shop/sander-mulder/pythagoras-stoel/
thingiverse
free
Pythagoras Mug
...pythagoras mug
thingiverse
this is a more recent attempt at a pythagoras cup that i modeled in blender 2.81.
thingiverse
free
PYTHAGORAS Representation by TECHB
...pythagoras representation by techb
thingiverse
pythagoras representation
thingiverse
free
pythagoras puzzle
...s puzzle
thingiverse
the classical pythagoras puzzle from 70-th
uses this model as a test of the precision of my new 3d printer.
thingiverse
free
Pythagoras by Pentoma
... lösungsprogrammen, bastelvorlagen, figurenvorlagen von legespielen wie tangram, soma-würfel, pentomino, hexiamond, tetrahex etc.
thingiverse
free
Pythagoras coffee cup by KIT_trainee_group
...
die kaffeetasse von pythagoras
im rahmen eines schulprojekts des kit
coffee cup of pythagoras
as part of a school project of kit
thingiverse
free
Pythagoras MUG by paulo2534
...34
thingiverse
mug version of the "pythagoras cup"
like my work and want to support me? consider buying me a cofee :)
thingiverse
free
Metaball Pythagora by VanlindtMarc
...metaball pythagora by vanlindtmarc
thingiverse
made with openscad
thingiverse
free
Pythagoras Mug by cecplays
...g, designed to keep the odd nature of the contraption hidden.
volume to overfill line, ~11.6 fluid ounces, or ~343.8 milliliters.
Lgbu
thingiverse
free
Pythagoras Tree 345 by lgbu
...ntentionally designed to overlap to a little bit for stability. easy to design in 123d design using the basic idea of similarity.
thingiverse
free
Chinese Lantern by lgbu
...the size needed. do use a raft for printing.
please note that the stl file is pretty big, around 100 mb because of the structure.
thingiverse
free
Tetrahedron, Triangular Pyramid Puzzle by lgbu
...giverse so i decided to make one. you need to print 4 copies of the same piece to make a triangular pyramid. great for all ages!
thingiverse
free
Pythagoras Tree (1:1:Sqrt2) by lgbu
...ap a little bit. the structure is very easy to design in 123d design using the basic idea of similarity. yes, this is a fractal.
thingiverse
free
Golden Curve/Spiral by lgbu
...ometric representations. the curve, of course, has interesting properties that are worthwhile for a k-12 steam class. have fun!
thingiverse
free
Hyperboloid Container / Caddy by lgbu
...s 45 degrees. the height of the resulting hyperboloid is about 74 mm. it is made of 18 or 36 copies of two symmetrical rulings.
thingiverse
free
Ceiling Hooks by lgbu
...asurement.
among the files are four ceiling hooks of various widths, a length of 70 mm, and a depth of 12 mm. the slot is 3mm.
thingiverse
free
Parallelogram Area Formula, Why? by lgbu
.... this can be further used to find the areas of many other shapes such as trapezoids, triangles, and even circles. have fun!
thingiverse
free
Hexagonal Chain Mail Interlocking Patterns by lgbu
...e as it is, it shows the value and fun of 3d design and printing. the 123d file is included so you could tweak it as you please.
thingiverse
free
Simple Tessellation Pattern by lgbu
...e included. it measures about 96 mm x 50 mm and 3.6 mm thick. six copies will be a good starting point (see pictures posted).
Pythagorean
turbosquid
$5
Pythagorean Cup
... 3d model pythagorean cup for download as ige, stl, and sldpr on turbosquid: 3d models for games, architecture, videos. (1501289)
sketchfab
$15
Pythagorean Theorem
... in literature, plays, musicals, songs, stamps, and cartoons abound. - pythagorean theorem - buy royalty free 3d model by arloopa
thingiverse
free
Pythagorean Cup by dangreinke
... itself by a siphoning effect once filled beyond a certain point. be prepared for a mess!
this cup was designed using fusion 360.
thingiverse
free
Pythagorean Cup by Conceptualiz3D
...pythagorean cup by conceptualiz3d
thingiverse
born cupped and died cupped
thingiverse
free
Pythagorean Espresso cup by Printrind
...s is a funny pythagorean espresso-cup with the drainpipe hidden in the handle. the right thing for your guests at a dinner-party!
thingiverse
free
Pythagorean Puzzle by UMF3D
...thagorean theorem by using the pieces from 2 smaller sides to create the hypotenuse squared.
c. heckley & g. wright, may 2018
thingiverse
free
Multi Purpose Pythagorean Cup by tweeto
...pose (3 modes) pythagorean cup:
fixed level - no cap
regular cup - fully closed cap
pythagorean cup - slightly opened cap (+2 mm)
thingiverse
free
Pythagorean 3x4 = 5 by KySyth
...pythagorean 3x4 = 5 by kysyth
thingiverse
not tested
thingiverse
free
PYTHAGOREAN CUP without central pin by luks3D
...pythagorean cup without central pin by luks3d
thingiverse
pythagorean cup without central pin
thingiverse
free
Devious Pythagorean Cup - Holy Grail by davidscanlan
...devious pythagorean cup - holy grail by davidscanlan
thingiverse
a remix of the devious pythagorean cup design
Theorem
3d_export
$10
theorem brass table lamp
...ww.crateandbarrel.com/theorem-polished-nickel-desk-lamp/s647448 date: 2022.1.3 viruses: clean, tested by prunescene! preview: yes
3ddd
$1
THEOREME modular sectional
... угловой
http://www.roche-bobois.com/#/en-jo/products/all/sofas/all/all/all/81628/fullscreen/
sketchfab
$15
Pythagorean Theorem
... in literature, plays, musicals, songs, stamps, and cartoons abound. - pythagorean theorem - buy royalty free 3d model by arloopa
thingiverse
free
Pythagorean theorem in 3D
...f the prism. it shows how the pythagorean theorem works to find the diagonal of an object in three dimensions. k.walton, 12/19/19
thingiverse
free
Pythagorean Theorem by MaximusG
...two of the bases. the base file is ptb, standing for pythagorean theorem base. this is perfect to teach kids about this equation.
thingiverse
free
Pythagorean theorem box by anthonywongseen
...ting the pythagorean theorem for a colleague who teaches mathematics. i guess students could build and design the box themselves.
3d_sky
free
Office Chair "Theorem".
...office chair "theorem".
3dsky
chair
office chair "theorem". 3dsmax 2009 64 + vray. with textures.
thingiverse
free
Pythagoras puzzle (Pythagorean Theorem proof)
...puzzle to visualize and teach the pythagorean theorem.
additional info and version history at:https://gitlab.com/tickelton/things
thingiverse
free
The Pythagorean theorem by Peterschotte
... the boxes was colored and sealed with water resistant transparant tape. turning around makes the water fill 1 or 2 of the boxes.
3dbaza
$3
Theorem Polished Nickel Floor Lamp (325986)
...theorem polished nickel floor lamp (325986)
3dbaza
theorem polished nickel floor lamp 3d model<br>sku: 648231
Dissection
turbosquid
$300
rudbeckia dissected
...d model rudbeckia dissected for download as max, obj, and fbx on turbosquid: 3d models for games, architecture, videos. (1182363)
turbosquid
$460
flowerbed of rudbeckia dissected
...rbed of rudbeckia dissected for download as max, obj, and fbx on turbosquid: 3d models for games, architecture, videos. (1182360)
turbosquid
$200
Human Heart Dissection Detailed
...uman heart dissection for download as ma, obj, fbx, and blend on turbosquid: 3d models for games, architecture, videos. (1361664)
turbosquid
$150
Human Skin Detailed Dissection
...n detailed dissection for download as ma, obj, fbx, and blend on turbosquid: 3d models for games, architecture, videos. (1366704)
turbosquid
$190
Male and Female Reproductive System Dissection
...ive system dissection for download as ma, obj, fbx, and blend on turbosquid: 3d models for games, architecture, videos. (1371212)
3d_export
$179
Anatomy Dissection laboratory
...nimum of polygons -scene fully configured and ready to render. -no photoshop on the preview -scene for 3ds max 2012 and v-ray 2.0
3d_export
$249
Human Anatomy Dissection Laboratory
...e made carefully with a minimum of polygons > -scene fully configured and ready to render. > -no photoshop on the preview.
3d_export
$15
Autopsy Table Roll-In with Down-Draft-System
...table roll-in with down-draft-system 3dexport autopsy table roll-in with dissection table professional autopsy tables with integrated exhaust system serve...
3d_export
$144
kaws flayed companion
...ave mirror modifiers and share the same uv coordinates (2500 verts each)<br>ready to visualization in cycles render engine.
3d_export
$97
kaws flayed lowpoly pbr
...maps. title is rendered in eevee, product pictures are rendered in cycles. ready for visualization in cycles/eevee render engine.
Hinges
3d_export
$10
hinge and hinge 148 specifications
...hinge and hinge 148 specifications
3dexport
hinge and hinge (148 specifications)
3d_export
free
hinge
...hinge
3dexport
hinge model
3ddd
free
hinges
...hinges
3ddd
крепление
two types of hinge for furniture.
3d_export
$6
Hinge
...hinge
3dexport
hinge assembly render 3d modelling design
turbosquid
$19
Hinges
...
turbosquid
royalty free 3d model hinges for download as max on turbosquid: 3d models for games, architecture, videos. (1453553)
turbosquid
$19
Hinges
...
turbosquid
royalty free 3d model hinges for download as max on turbosquid: 3d models for games, architecture, videos. (1447125)
3d_export
$5
hinge 1
...hinge 1
3dexport
hinge 1
3d_export
$5
hinge 2
...hinge 2
3dexport
hinge 2
3d_export
$5
hinge 3
...hinge 3
3dexport
hinge 3
3d_export
$5
hinge 4
...hinge 4
3dexport
hinge 4