Simple Stop Motion with ffmpeg
Andrew Lindesay has a nice script for simple script for using ffmpeg to do stop motion:
ffmpeg -framerate 10 \
-pattern_type glob -i '*.JPG' \
-vf scale=640:-1 -c:v libx264 -pix_fmt yuv420p \
out.mp4
This works great for compiling photos shot by a GoPro!
The shots are labelled chronologically by frame number:
G0107340.JPG
G0107341.JPG
G0107342.JPG
G0107343.JPG
G0107344.JPG
G0107345.JPG
G0107346.JPG
G0107347.JPG
G0107348.JPG
G0107349.JPG
So, the -pattern_type glob -i '*.JPG'
argument picks them up in order.
The argument scale 640:-1
automatically resizes frames to 640xY and preserves the aspect ratio. This might not be what you want, but it makes for small videos.
Interview with Conway
The Simons Foundation has a lovely series of interview with John Conway.
Lots of stories and insights. He lead a storied life.
Math Club Geometry Training Session
These are some questions that I prepared for Math Club. The problems follow Paul Zeitz’s excellent book The Art and Craft of Problem Solving. You can find this hand-out is here:
https://pgadey.ca/teaching/2019-math-club/geometry-training-talk/geometry-training-talk.pdf (tex)
1. Advice and Suggestions
- Draw big diagrams. Lots of them.
- Use multiple colours to keep track on information.
- Draw several examples with different lengths/angles.
- Avoid coordinates.
2. Facts and Questions
Fact 1 Congurence conditions for triangles: (SAS, ASA, SSS, AAS)
Side-angle-side, angle-side-angle, side-side-side, angle-angle-side.
Question 2 Why is angle-side-side not a congruence condition?
Question 4 Show that
using the Fact~3.
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Fact 5 (Transversals)
and
are parallel iff
.
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Question 6 Show that the sum of the interior angles of a triangle is
. (Idea: Add a new parallel line.)
Question 7 For any triangle
, the exterior angle at
is the sum of the interior angles at
and
.
Question 8 (Parallelograms) Use congruence and parallels to show:
- The opposite sides of a parallelogram have the same length.
- The opposite angles of a parallelogram are equal, and adjacent angles are “supplementary” (sum to
).
- The diagonals of a parallelogram bisect each other.
(Idea: Introduce triangles.)
Question 9 (Isoceles triangles) A triangle
is isoceles if
. Show that: If
is isoceles then
.
Question 10 Let
be a triangle. Let
,
, and
be the midpoints of
,
, and
respectively. Show that the lines:
,
, and
, dissect
in to congruent triangles.
(Big Idea: Introduce parallels to
and
at
. These will create new “phantom points” on
and
. These new points will be very helpful because of our theory of parallelograms.)
Fact 11 (Circles and Chords) If any two are true, then all three are true.
- The line passes through the center of the circle.
- The line passes through the midpoint of the chord.
- The line line is perpendicular to the chord.
Fact 12 (Circles and Tangents) A tangent to a circle is perpendicular to the radius at the point of tangency. Also, a perpendicular to a tangent line placed at the point of tangency, will pass through the center of the center of the circle.
Question 13 Suppose that
is outside a circle. If
and
are tangent to the circle, then
.
Question 14 (Inscribed Angle Theorem) Consider a circle centered at
with points
on the perimeter of the circle. Show that
. (Idea: Chase angles.)
Question 15 Consider a semi-circle with base
.
Ifis on the perimeter of the semi-circle, show that
.
Question 16 (Circumcircles) The circumcircle of a triangle
is a circle passing through
,
, and
.
- Suppose that a circumcircle exists. Show that its center is the intersection point of the perpendicular bisectors of the sides of the triangle. (If a circumcircle exists, then it has a unique center.)
- Given a triangle, any two perpendicular bisectors will intersect in a point equidistant from all three vertices. (Any triangle has a circumcenter.)
- All three perpendicular bisectors intersect in a unique point, the “circumcenter”.
Question 17 (Incircles) The incircle of a triangle
is a circle tangent to
,
, and
.
- Suppose that an incircle exists. Show that its center is the intersection of any two angle bisectors.
- Show that the intersection of any two angle bisectors is the center of an incircle and this point is unique.
- All three angle bisectors intersect in a unique point, the “incenter”.
3. Contest Problems
Question 18 (Canada 1991) Let
be a circle and
a point in the plain. Each line through
that interesects
determines a chord of
. Show that the midpoints of these chords form a circle.
Question 19 (Rochester 2012) Let
be an isoceles triangle with
and
. Consider and interior point of this triangle such that
and
. Find with proof, the measure
.
Question 20 (Rochester 2013) Let
be a triangle with
. Suppose the bisectors of
,
, and
meet
,
, and
at points
,
,
, respectively. Prove that
is a right angled triangle.
MAT B41 — Week 8
Additional resources:
- Khan Academy on multivariate maxima and minima.
- Kristal King on local extrema.
Suggested Exercises:
- Course Notes: Quadratic forms and determinants
- 3.3 Extrema of Real-Valued Functions: 1,2,3,11,13,21,29,31,52
Past Finals:
- Final 2015: Let
. Find and classify the critical points of
.
- Final 2016: Let
. Find and classify the critical points of
.
Notes:
MAT B41 — Week 7

Midterms are graded! New list of suggested exercises is available!
There is a new list of suggested exercises available here.
Suggested Exercises
- Chapter 1 Review (p. 71): 1, 4, 5, 7, 8, 16, 18, 20
- Chapter 2 Review (p. 145): 1, 2, 3, 5, 6, 10, 15, 25
STLHE 2018 — Day 0 — Introduction
I am currently at Scholarship of Teaching and Learning in Higher Education 2018 in Sherbrooke, QC. The plan is to post a short little video everyday of the conference to keep people updated on how things are going. Stay tuned!
MAT B41 — Week 6
Term Test is this Friday. Reading week is next week!
We have a modified class schedule this week.
- Tuesday: Taylor Series and Review.
- Thursday: Class Survey and Work Period, everyone is invited to bring problems to practice.
- Friday: Term Test, will be held Friday afternoon.
Term Test Policy
From the Course Syllabus, we have the following policy:
The Term Test will be written outside of regular lecture hours. If you cannot attend reasons of creed or religion, then you will must contact Parker as early as possible to arrange for an alternative sitting. If you miss the midterm test for medical reasons, you must contact Parker within 24 hours of the test.
You will need to send a UTSC Verification of Student Illness or Injury form:
Students who miss the midterm test will be asked to provide the Verification Form and a timetable for the next five days. You will be given only one opportunity to write the make-up test.
Parker scheduled to the midterm to avoid Ramadan, but he forgot about Eid Al-Fitr. If you want to celebrate Eid with your family, instead of writing the midterm at the usual time, please contact Parker immediately.
The Week after Reading Week!
Parker will be traveling to STLHE 2018 and the IBL Workshop.
Our Tuesday evening lecture will be delivered by Ivan Khatchatourian.
Our Thursday morning lecture will be delivered by Ray Grinnell.
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