. Syllables that are short by nature are held for the length of one mora, which is analogous to a crotchet, or a quarter note, in music.
Figure 3: The crotchet is analogous to a syllable of length one mora.
Obscure Syllables:
In Ancient Greek, iota subscripts are considered to be obscure syllables:
ᾳ , ῃ , ῳ
. In Ancient Greek, the above iotas are pronounced:
/ˈaː.ɪ/ , /ˈeː.ɪ/ , /ˈˈɔː.ɪ/
, or:
/ˈaː.(ɪ)/ , /ˈeː.(ɪ)/ , /ˈˈɔː.(ɪ)/
, or:
/ˈaː.ɪ/ , /ˈeː.ɪ/ , /ˈˈɔː.ɪ/
. Obscure syllables are so short, that their value – in terms of morae – is not reckoned. Obscure syllables are zero morae in length. This is analogous to a grace note in music.
Figure 4: The grace note is analogous to a syllable of length zero morae.
Conclusion:
Knowing how to identify long and short syllables in Ancient Greek will aid us in our study of accentuation – which is the study of which syllables to stress, and which syllables to leave unstressed – and contonation – which is the study of the rise and fall of pitch across Ancient-Greek syllables.
The Naming of Sets in Set Theory Figure 1: I drew this set-naming italic character in SVG. You may view the code of this image at my Codepen Account . Figure 2: What the SVG image looks like when exported as a PNG. [1] In Set Theory - which underpins so much of computing mathematics - we conventionally name sets with capital italic letters. In computer science, a name such as: A , would be termed an: ‘identifier’ . In the below example, we shall use the capital italic character: R so as to name the members of the set of Radix-ten [2] integers. Figure 3: “ A SQUARE-ROOT SIGN This sign is from radix (Latin for root) and was first used by Leonardo da Pisa in 1220. Today’s √ sign, which may be a distortion of the letter “r”, is sixteenth-century German.” [3] An Example of Naming a Set with an Italic Italic Capital Character
Introduction to Modern Geometry Modern Geometry: The Directed Line Segment In Euclidean Geometry, line segments possess only magnitude, and not direction. A B Figure 1: In Euclidean Geometry, only the magnitude of line segments is considered. As we can see in Figure 1 , in Euclidean Geometry, the line segment: |AB| would be considered equal to the line segment: |BA| . However, this is not the case with Modern Geometry. In Modern Geometry, line segments not only possess magnitude, but direction also. A B Figure 2: In Modern Geometry, line segments possess direction as well as magnitude. In Modern Geometry: |AB| is termed: ‘a directed line segment’ . A B Fig
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