Part 1 of 5 Equilateral triangle - Area - ratio

Without using trigonometry, I've solved a geometry problem concerning equilateral triangle. As seen in part 4 and 5, the original problem is to determine the ratio of two areas, the equilateral and the quadrilateral embedded. Since I tried my best to stick to the elementary method, it took me 7 videos ,which has something connected with each other, to present the whole package of solutions.

However each of them can be considered as an independent problem and solution. Including the word processing and the preparations of those videos, it took me more than 100 hours in 50 days to finish the whole task(including part 1 to 5 and others).

Somebody would ask me why I spent so much energy to present this problem and solution in so much detail. I would like to tell them this is to show that there are so many difficulties behind such kind of simple high school Math problem. This is about the area of Psychology for learning. Two technical terms can give the readers some hints: Zone of Proximal development(from Vygotsky), Hierarchy of intellectual skills(from Robert Gagné).

By the way, I would like to introduce a term, shuxue to the English-speaking world. Shuxue is a phonetic transcriptions of 2 Chinese characters which is exactly the term representing Mathematics.

Category:

Education

Tags:

• Mathematics
• Educational
• Psychology
• Geometry
• learning
• strategies
• problem
• solving
• education
• equilateral
• triangle
• right-angled
• triangles
• ratios
• area
• congruence
• similar
• trapezium
• intercept
• theorem
• PytharorasTheorem
• elementary
• method
• logical
• thinking
• hierarchy
• of
• intellectual
• skills
• heuristics
• George
• Pólya
• Vygotksy
• ZPD
• Scaffolding
• Robert
• Gagné
• task
• analysis
• Shuxue
• Jihexue

[UrduWiki]

I usually don't take time to post comments. But this is an exception. I just wanted to say that I am an Engineer going back to school after 12 years for further studies.

Having forgotten the basics, your video- even it was posted nearly 2 years ago- was probably one of the best help sources I gathered to refresh my math skills. I really appreciate and want you to know how much your hardwork is being appreciated. God bless you.

[rehcaethtam]

@UrduWiki Thank you for your great encouragement?

Parts 1 through 3 are prelude to the original problem appearing in part 4 (part 5 is alternative solution to the same problem).

If you have time, I recommend you spend some time "reading" part 4 or 5.

[cheerdelle100]

the 1 person who dislike is your trigonometry teacher :|

[HappyBirthdaySANTA]

I think it's the song from candyman the movie

[pinkfrosting12]

What song is playing in the video?

[erauqscme]

Thank you very much for your comment!

Since I majored in Sociology, from which I have also benefited a lot. However I did not take any Math subjects in University, except for statistics for Social Science faculty.

Therefore, I would take your positive comment as moral support, which would stimulate me to further efforts and keep up constant improvement in teaching method of Math.

[TheFallibleFiend]

I like the concept of this kind of teaching method.