Download Applied Math in Haircutting

Applied Math in
Haircutting
The Celestial System Approach
Hair Cutting
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In the artist world, hair cutting is considered
an art form, like a sculptor carving out the
desired shape.
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At a closer look, one will find that basic
geometry and trigonometry play a vital role in
the fundamentals of hair cutting
Art and Science!
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Art in hair cutting: A 3-D form
to sculpt
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Includes: hair lengths,
textures, growth patterns,
density, and elasticity
which all determine the
outcome of a hair cut.
Cosmetologists must learn to
combine the art and creativity
involved in haircutting with the
fundamentals of geometrical
angles, shapes in
trigonometry, and the
principles of applied math.
Celestial Axis in Haircutting
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Celestial Axis - an
imaginary sphere used as
a background for locating
positions in space.
Use in hair cutting to
Identify straight and
curved lines formed
around the shape of the
head
Celestial Axis as a Guide in
Hair Cutting
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The celestial axis
assists in…
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identifying parts,
sections, angles,
degrees, and the
direction of movement.
The axis provides a
guide to create various
hair cutting forms.
Celestial Axis on Head Form
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For reference points in
hair cutting, imagine a
grid on the scalp.
Using the imaginary
grid as a guide, lines,
angles and degrees
can be identified on the
head.
Geometry in Haircutting
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Horizontal lines run parallel,
(east and west), creating the
illusion of added weight.
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Example: One Length
Haircut
Vertical lines run
perpendicular (north and
south), creating the illusion
of removing weight.
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Example: Layered Haircut.
Geometry-Creating Diagonal Lines in
Haircutting
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Diagonal Lines run between
horizontal and vertical lines
–
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create the illusion of less
weight in a haircut.
Diagonal Lines in haircutting
create a angle, depending
on finger position.
Beveling - a technique used
in diagonal lines to create a
stack appearance in hair.
Trigonometry in Haircutting

Trigonometry - the study of
curved space, such as a
head form.

Angles are used in
haircutting as reference
points of how to envision the
hair before cutting.
– Examples: 0°, 45°,
90°,135°,180°
Concave and Convex Lines in
Haircutting
Concave Lines
•Used to create a curve
like an arch.
•Most often used in the
back of the head,
around ears, and bang
area, (also called fringe)
Convex Lines
 used to create a “U” or “V”
shape in haircutting.
–
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The center of the convex line
creates the illusion of weight.
The area of weight in any
haircut will be the focal
point.
One of the goals in
haircutting, is to maximize a
clients good features and
minimize any poor features.
–
Convex lines can minimize
broad shoulders.
Angles Used in Haircutting
Angle
Creates...
Illusions
Examples
Zero
Horizontal lines in
haircutting
1. Weight or fullness
2. Rectangle or oval
form
One-Length Cuts
45°
A stack or wedge
Weight lines should
reflect positive
facial features
Triangle Forms
90°
Hair that is the same
lengths in that
area, called a
uniform cut
1. More width
2. Make the face
appear more
round
Circular Forms
180°
Layered hair, start
below the crown
and progress to
end length
Fullness and body
Oval Forms
Reference Points Used in Haircutting
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Parietal Ridge- Widest area of the head.
–
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Occipital Bone- Bone that protrudes at the base of
the skull.
Apex- Highest point on the head.
–
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Area used to measure for wig size, custom hats, and baby
developmental growth.
Found by placing a comb flat on the top of the head. The
highest point, is where the comb rest on the head, laying
horizontally.
Four Corners- Shows where the head begins to
curve on each side of the head, from flat to round.
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Used mostly for determining reference points for bangs.
Reference Points of the Head
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Crown- Area between the apex and occipital bone.
Different hair growth patterns exist in this area,
requiring caution when cutting hair.
Top- Area between the top of the forehead and the
crown.
Sides- Area from the back of the ear towards the
face and is below the parietal ridge.
Nape- Area below the occipital bone to neckline.
Working Areas of the Head
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Sections- Hair is parted in working areas for ease
and better results in haircutting.
Subsections- Sections divided into smaller areas.
Parting- A line, horizontal, vertical or diagonal used
to separate the subsection.
Elevation/Projection- The angle or degree the hair
is held, in relation to the head.
Tension- Amount of pressure used when holding
hair between fingers while cutting hair.
Haircutting Lines
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Cutting line- is the angle the fingers are held
when cutting hair. Also called finger position.
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Guideline- is the first cut taken to use as a
reference for the rest of the hair. Also called the
guide. Determines length that will be cut.
Two Types of Guidelines
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Traveling Guideline- Taking
a small piece of the previous
hair cut to use as a guide for
the next area to be cut. Also
called movable guide.
Stationary GuidelineSections are combed to one
area to be cut. The guide
does not move.
Distribution
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Distribution - the direction the hair is combed from the parting.
Natural Distribution- the direction the hair naturally falls from
the curve of the head.
Perpendicular Distribution- is achieved by combing the hair
straight out from the head, using a 90° angle.
Shifted Distribution- Used for length increases and blending
from one area to another.
Directional Distribution- The hair is combed straight up or out
from the curve of the head. Length increase will be the result
cut.
Head Position in Haircutting
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Upright Head Position- Used for
hair length
above the shoulders.
Forward Head Position- Used
when a beveled haircut is
desired. Recommended when
cutting hair below the shoulders
in the back area.
Titled Head Position- Used
when working on the sides of
the head for comfort and ease
for the cosmetologists to better
see the working area.
Partings
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Partings – Lines that subdivide the hair
so the hair is easier to control.
Partings are generally parallel to the
guideline.
Partings can be horizontal, vertical, diagonal
forward, diagonal back, concave, convex,
curved or zigzag.
Finger Position
Finger position is in relation to the parting.
The direction the hair is held.Two types are
used:
 Parallel Finger Position - Fingers are
positioned same direction as parting.
 Non-Parallel Finger Position- Fingers are
positioned unequally to the part. The position
used will determine the line cut.
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Crosschecking Haircuts
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Crosschecking is a term
used to make sure the hair
is cut correctly.
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Check a haircut for balance
and accuracy, use the
opposite parting
implemented in the haircut.
Example: If the haircut was
performed with horizontal
partings, check for
accuracy using large
sections and vertical
partings.
Work Cited
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Milady’s Standard
Textbook, copyright
2004
Salon Fundamentals
Textbook, copyright
2000