The words pi, pie, pye sound the same but have different meanings and spellings. Why do pi, pie, pye sound the same even though they are completely different words?
The answer is simple: pi, pie, pye are homophones of the English language.
To jumble or mix up (type).
To become jumbled.
The 16th letter of the Greek alphabet. See Table at alphabet.
Mathematics A transcendental number, approximately 3.14159, represented by the symbol π, that expresses the ratio of the circumference to the diameter of a circle and appears as a constant in many mathematical expressions.
A baked food composed of a pastry shell filled with fruit, meat, cheese, or other ingredients, and usually covered with a pastry crust.
A layer cake having cream, custard, or jelly filling.
A whole that can be shared: "That would . . . enlarge the economic pie by making the most productive use of every investment dollar” ( New York Times).
pie in the sky An empty wish or promise: "To outlaw deficits . . . is pie in the sky” ( Howard H. Baker, Jr.)
Archaic spelling of pie (the pastry food).
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from Wiktionary, Creative Commons Attribution/Share-Alike License and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").