This document discusses the math behind 3D printing. It explains that 3D printing involves constructing a three-dimensional object from a CAD model by depositing and joining material under computer control. The document outlines that several areas of math are important for 3D printing, including geometry, trigonometry, calculus, linear algebra, and topology. It provides examples of how each area of math is used, such as using geometry to create 3D models, trigonometry to calculate angles and distances, and calculus to optimize the printing process. The document also briefly discusses current and potential future applications of 3D printing.

1. Made & Presented By: Rithvik Lingala (6th Grader in 7th Grade GT Math)
MATH BEHIND
3D
PRINTING

2. What Is 3D Printing?
2
● The construction of a three-dimensional
object from a CAD model
● It can be done in a variety of processes
● Material is deposited & joined under
computer control

3. Math In 3D Printing
There are many subjects of math in 3D
printing.
01 02 03
Geometry Trigonometry Calculus
3
05
Linear
Algebra
Topology
04

4. 4
● Deals with the properties of shapes
● Deals with relationships of shapes &
spaces
● In 3D printing, geometry is used to
create and manipulate 3D models.
Geometry In 3D
Printing

5. 5
● Deals with the relationships between
angles and sides of triangles
● Extensively used to calculate angles and
distances between points
● Important for creating accurate and
precise models
Trigonometry In 3D
Printing

6. 6
● Deals with the study of rates of change
and accumulation
● Used to calculate the rate at which
material is deposited
● Important for optimizing the printing
process and achieving the desired level
of detail
Calculus In 3D
Printing

7. 7
● Deals with the study of linear equations
and their properties
● Used to calculate the position and
orientation of objects in 3D space
● Important for ensuring that the printed
object is in the correct position and
orientation
Linear Algebra In 3D
Printing

8. 8
● Deals with the study of the properties
of spaces that are preserved under
continuous transformations
● Used to ensure that the model has no
holes or gaps
● Enables lighter-weight parts using less
material
Topology In 3D
Printing

9. 9
INTERACTIVE
TIME

10. 10
MODEL
COMPARISON

11. 3D Printing Today & Tomorrow
Design
Prototype
Healthcare
Architecture
Education
11

12. Citations
12
Project, C. (n.d.).
3D Printing: The
Steps Needed
and The Math
Involved.
prezi.com.
https://prezi.com/
co6t1odsdcjg/3d-
printing-the-step
s-needed-and-the
-math-involved/
Muthu, G. (n.d.).
Mathematics in
3D printing.
www.linkedin.c
om.
https://www.link
edin.com/pulse/
mathematics-3d
-printing-geetha
-muthu#:
Wikipedia
contributors.
(2023). 3D
modeling.
Wikipedia.
https://en.wikip
edia.org/wiki/3D
_modeling#:

13. Citations
13
Multimedia
Applications
Division Freescale
Semiconductor,
Inc. (2010, May). 3D
math overview and
3D graphics
foundations. NXP.
Retrieved October
18, 2023, from
https://www.nxp.co
m/docs/en/applicati
on-note/AN4132.pd
f
Mathematics for
Computer
Graphics. (n.d.).
https://faculty.c
c.gatech.edu/~t
urk/math_gr.ht
ml
Math for
Computer
Graphics. (n.d.).
https://faculty.c
c.gatech.edu/~t
urk/math_gr_ne
w.html#:

14. Citations
14
Scale Factor -
formula,
meaning,
examples.
(n.d.). Cuemath.
https://www.cue
math.com/geom
etry/scale-facto
r/#:
Wikipedia
contributors.
(2023b, October
7). 3D scanning.
Retrieved from
https://en.wikip
edia.org/wiki/3D
_scanning#:~

15. 15
THANK
YOU
Any Questions?