The blog
A casual blog designed as a regular supplement to a standard Philippine high school mathlete's training.
The name
PHI is the call sign of the Philippines in the International Mathematical Olympiad. It is then a happy coincidence that "phi" is the transliteration of the Greek letter Φ, the lowercase version of which is used (among other purposes) to denote the number $\varphi=(1+\sqrt{5})/2$, known commonly as the Golden Ratio, which supposedly lies at the heart of our sense of natural aesthetics.
The letter Φ is also a perfect starting point for the logo, which attempts to capture the impetus of the blog to illustrate the hidden half of the problem-solving process.
The name
PHI is the call sign of the Philippines in the International Mathematical Olympiad. It is then a happy coincidence that "phi" is the transliteration of the Greek letter Φ, the lowercase version of which is used (among other purposes) to denote the number $\varphi=(1+\sqrt{5})/2$, known commonly as the Golden Ratio, which supposedly lies at the heart of our sense of natural aesthetics.
The letter Φ is also a perfect starting point for the logo, which attempts to capture the impetus of the blog to illustrate the hidden half of the problem-solving process.
Features
- Problem discussions every now and then.
- Laconic Solution Sketch: The solution reduced to a one-liner for advanced readers, or those in a hurry, or those who just need a push in the right direction.
- The Codex features essential theorems and results.
- Feature articles and series here and there, especially during contest season in the Philippines.
- PDF downloads of many new posts.
The premise
A decade of involvement in the quaint field of competitive maths has taught me one thing:
That hidden half of the story is at the core of this blog. In each problem discussion, I will chronicle in detail how one goes about solving a famous or otherwise notable problem. As much as possible, I will avoid routine problems; I expect the audience to handle those themselves. Every post will have some sort of takeaway - a nice tool, an important theorem, or a good way of thinking.
The scope and tone
Wherever topics exotic to the standard contest repertoire are tackled, I will provide links for clarification and practice. Problem difficulty should be comparable to AIME; discussions, however, are made to be comprehensible even to first year high school mathletes.
Some new high schoolers inevitably find it difficult to transit from "pattern finding" grade school maths to "critical reasoning" high school maths. The jump from largely intuitive grade school concepts to mathematical formalism can be off-putting for many. The esoteric vocabulary and language of most high school solutions doesn't help either.
I acknowledge this, and try to ease the shift. I'll be using a colloquial tone as much as possible, without losing the essence of the mathematics. Think xkcd's What If. Of course, actual solutions will be written in proper "solutionese", which by then would have been illuminated by the preceding discussion.
A solution tells only half the story.There is an entire art behind how to think efficiently, to approach a problem correctly and attack it with an economy of mental resources. Almost none of this will survive into the final solution; in solution writing, brevity is virtue.
That hidden half of the story is at the core of this blog. In each problem discussion, I will chronicle in detail how one goes about solving a famous or otherwise notable problem. As much as possible, I will avoid routine problems; I expect the audience to handle those themselves. Every post will have some sort of takeaway - a nice tool, an important theorem, or a good way of thinking.
The scope and tone
Wherever topics exotic to the standard contest repertoire are tackled, I will provide links for clarification and practice. Problem difficulty should be comparable to AIME; discussions, however, are made to be comprehensible even to first year high school mathletes.
Some new high schoolers inevitably find it difficult to transit from "pattern finding" grade school maths to "critical reasoning" high school maths. The jump from largely intuitive grade school concepts to mathematical formalism can be off-putting for many. The esoteric vocabulary and language of most high school solutions doesn't help either.
I acknowledge this, and try to ease the shift. I'll be using a colloquial tone as much as possible, without losing the essence of the mathematics. Think xkcd's What If. Of course, actual solutions will be written in proper "solutionese", which by then would have been illuminated by the preceding discussion.
The author
I am Henry Morco, currently a university student. Over eleven years of competing in mathematics I've amassed a decent corpus of experience and recognition in both in the local and the international scenes (e.g. Champion, PMO 2013; Silver, APMO 2013; Bronze, IMO 2012).
I enjoy reading, coding, and dabbling in the occasional math problem.
Minutiae
Unless I say so, all solutions in this blog are my original work.
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