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.

https://www.simonsfoundation.org/2014/04/04/john-conway/

Polya on Guessing

Polya Guessing from ihor charischak on Vimeo.

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?

Fact 3 If an angle measures a straight line, then .

Question 4 Show that using the Fact~3.

Fact 5 (Transversals) and are parallel iff .

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 .
If is 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

Parker comes back! Public lecture on Friday in IC 200 at 11am.

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:

• Tabeeb’s notes
• Parker’s 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!

Mid-Course Survey

The mid-course survey is available here.

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:

http://www.utsc.utoronto.ca/∼Eregistrar/resources/pdfgeneral/UTSCmedicalcertificate.pdf

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.

MAT B41 — Mock Midterm!

Mock Midterm was today in IC 130. Midterm Test next week!