The star and crescent are Muslim symbols ...

this is not true because star is not islamic symbol. you cannot say it is by looking at some arabic countries' flags because today's many arabic countries inspired frm Turkish Rebuclic and its cuz of the respect for Turks in islamic world.

abt flag's inspiration of Byzantine...

this is not true also. becuase Turks NEVER inspired frm any other country on flag. NEVER. because for Turks flag is different. Flag means everything such as honour, fame, culture, language and nation.

Many traditions explain the star and crescent symbol. It is known that Diana (Artemis) was the patron goddess of Byzantium and that her symbol was a moon. In 330, the Emperor Constantine rededicated the city - which he called Constantinople (today's Istanbul) - to the Virgin Mary, whose star symbol was superimposed over the crescent. In 1453 Constantinople (Istanbul) was captured by the Ottoman Turks and renamed Istanbul, but its new rulers may have adopted the existing emblem for their own use"

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Historical facts:
"Red has been prominent in Turkish flags for 700 years. The star and crescent are Muslim symbols, but also have a long pre-Islamic past in Asia Minor. The basic form of the national flag was apparently established in 1793 under Ottoman Sultan Selim III, when the green flags used by the navy were changed to red and a white crescent and multi-pointed star were added. The five-pointed star dates from approximately 1844. Except for the issuance of design specifications, no change was made when the Ottoman Empire became the Republic of Turkey and the Caliphate (religious authority) was terminated by Ataturk.

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Legends:
"A reflection of the moon occulting a star, appearing in pools of blood after the battle of Kosovo in 1448, the battle during which the Ottomans defeated the Christian forces and established the Ottoman Empire in Eastern Europe until the end of the 19th century, led to the adoption of the Turkish flag by Sultan Murad II according to one legend. Others refer to a dream of the first Ottoman Sultan in which a crescent and star appeared from his chest and expanded, presaging the dynasty's seizure of Constantinople (Istanbul). There are other legends explaining the flag."

Meaning of the flag
It's very difficult to explain the real meaning of a flag; there are legends, actual stories, and outright misinformation about the reason of certain colors or designs were put on national flags. Also individuals may have their own interpretation of their own national flag. Religious symbolism can also be expressed via color, such as the crescent moon which is a traditional Islamic symbol.