Both scientific and artistic considerations went into the making of Hangeul, but perhaps the most influential aspect was the oriental philosophy including concepts like Yin and Yang, Ohaeng (The Five Elements) and Cheonjiin (Heaven, Earth and Man).
If you get an appreciation for the philosophical elements, learning Hangeul will be that much more fun!
To put it simply, Yin and Yang about a constant interaction of natural opposites. Things like dark and light, male and female, hot and cold. Nothing stands on its own, there must be harmony among all of these things. This theory was taken very seriously in the creation of Hangeul, and as a result every vowel must be accompanied with a consonant to make a syllable in Korean. No one letter can stand alone.
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The Five Elements theory states that everything in the universe is made up Fire, Earth, Metal, Water, and Wood. Each element has certain unique attributes relating to everything: colors, direction, fruits, seasons, and even the main letters in Hangeul. Each element has something that contributes to it's growth, and something that destroys it. In turn, it contributes to another element while it destroys another.
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It was a widely held Confucian belief during King Sejong's time that the world consisted of three things. Heaven, the earth and man, who served as a mediator between the two. This notion is called Cheonjiin. As you can see from the drawing, the symbol for heaven has become ".", earth became "ㅡ" and man is symbolized by "ㅣ". These symbols are the basis of vowels in Hangeul.