4. Educational Issue
—Focus on ADHD children
• Targeted Students: Attention-Deficit Hyperactivity
Disorder, also known as ADHD, is a very commonly
diagnosed disorder in young children. This Learning activity
mainly concentrates on the children with ADHD who find it
more difficult to focus and to complete their schoolwork in
the junior secondary school.
• Activity description: Within the art-combining
module, teachers would cultivate students to find out their
potential capacity in the scope of art, and then stimulate
them to integrate art with mathematics drawing, such
as, make use of Web2.0 graphing tool in mathematical
mapping instruction.
• Learning Outcome: ADHD children could calm down and sit
still to draw their mathematical mind.
5. Leonardo da Vinci
• There are many examples of artists
who have been inspired
by mathematics and studied
mathematics as a means of
complementing their works.
The Italian artist Leonardo da Vinci is
an good example.
Mona Lisa
• It has been acclaimed as "the best
known, the most visited, the most
written about, the most sung
about, the most parodied work of art
in the world."[
6. The Golden Triangle
• The overall shape of the
woman is a triangle
with her arms as the
base and her head as
the tip, drawing
attention to her face.
7. The Great Pyramids
• Evidence of mathematical
influences in art is present in
the Great Pyramids, built
by Egyptian Pharaoh Khufu and
completed in 2560BC.
Mathematics geometric
• Herodotus related in one
passage that the Egyptian priests
told him that the dimensions of
the Great Pyramid were so
chosen that the area of a square
whose side was the height of the
great pyramid equaled the area
of the triangle.
8. Kepler’s triangle or 3-4-5
triangle?
• While the exact triangle the
Egyptians chose to design
their pyramids after
remains unclear,
• the fact that the dimensions
of pyramids correspond so
strongly to a special right
triangle suggest a strong
mathematical influence in
the last standing ancient
wonder.
11. What do we mean by Simple Harmonic
Motion?
It is a type of periodic motion where the
restoring force is directly proportional to the
displacement.
Mathematically, the restoring force F is given by:
F = -kx
Where F is the restoring elastic force exerted by
the spring (in SI unit N) , k is the spring constant
(N m−1 ), and x is the displacement from the
equilibrium position.
12. Consider the following activity in the
webpage:
http://physics.bu.edu/~duffy/Ejs/EP_chapter1
2/reference_circle_v1.html
Right click and download the jar file into your
computer (or just run it directly as a web2.0
tool).
13. Click to show the Change to select
corresponding the corresponding
sine and cosine mass, amplitude, f
graph of S.H.M orce and phase of
S.H.M
Stimulation Click “play”
starts from to start the
zero stimulation
Click “Step
Forward” to
show stepwise
procedure of
S.H.M
14. How to play with the stimulation?
Step 1:Try to play the stimulation – Click the button “Play”.
Step 2: Press “Restart” button.
Step 3: Press “Play” button again. When it moves near starting
point, press “Step Forward” button step wisely until the starting
point.
We obtain the following figure:
15.
16. What does the above graph mean?
From the above graphs (position, velocity and
acceleration), we observe, both position and
acceleration are cosine graph.
However, velocity is a sine graph.
Therefore, we may have the following
assumption:
X(t) = Acosωt – function for displacement
V(t) = Aωsinωt – function for velocity
a(t) = -ω2 Acosωt – function for acceleration
17. Note: F = ma
X(t) = Acosωt
ma = -kx
By direct substitution, we have the following equality:
-ω2 Acosωt = - Acosωt
ω=
2
, ω=
ω = 2πf, f=
