Why does the supreme court refused to define the term republican form of government

Direct democracy is a form of government in which people vote directly on key issues and for their leaders. ... The framers of the constitution chose a republican form of government over a direct democracy because they feared putting important political matters directly in the hands of th

Supreme Court refused as to fear upon as in putting the imperative political set of matters directly in the hands.  

Direct democracy is defined as the medium of government into which the people will be voting straight on top of the key issues and for the side of the leaders. Framers by the side of constitution choose away with the republican form of government over a direct democracy as they are afraid of putting the important set of political matters.

can you show the map , i'll be able to update my answer