Christendom, in the widest sense, refers to Christianity as a territorial phenomenon: those countries where most people are Christians, or nominal Christians, are part of Christendom.
Christendom - Christendom as a polity.
In a more significant and meaningful sense, it refers to the medieval and renaissance notion of the Christian world as a sort of social and political polity. In essence, the vision of Christendom is a vision of a Christian theocracy, a government devoted to the enforcement of Chri ...
And here we go. This will be an inductive proof, providing a formula for f(n) in terms of f(n − 1).
In the figure you can see the dark lines connecting points 1 through 4 dividing the circle into 8 total regions (i.e., f(4) = 8). This figure illustrates the inductive step from n = 4 to n = 5 with the dashed lines. When the fifth point is added (i.e., when computing f(5) using f(4)), this results in four (n − 1) new lines (the dashed lines in the diagram) being a ...
In a more significant and meaningful sense, it refers to the medieval and renaissance notion of the Christian world as a sort of social and political polity. In essence, the vision of Christendom is a vision of a Christian theocracy, a government devoted to the enforcement of Christian values, and whose institutions are suffused with Christian piety. In this vision, members of the Christian clergy wield plenty of political clout. Secular rulers are their subordinates and agents; and national or political divisions are subsumed under the unit ...
If we already have n points on the circle and add one more point, we draw n lines from the new point to previously existing points. Two cases are possible. In the first case (a), the new line passes through a point where two or more of lines between previously existing points cross. In the second case (b), the new line crosses each of the old lines in a different point. It will be useful to know the following fact.
Lemma. We can choose the new point A so ...
Suppose you have a circle with n points lying on the perimeter of the circle and lines connecting all of the points. There are a total of
lines connecting the points. The mission is to find the maximum number f(n) of areas that the circle can be divided into, as a function of the number n of points.
For small values we have:
n = 0 or 1 gives f(0) = f(1) = 1;
f(2) = 2 because there is a single diameter, making two areas;
f(3) = 4; ...
The Latin term Corpus Christianum is often translated as the Christian body, meaning the community of all Christians.
It described the pre-modern notion of the community of all Christians united under the Roman Catholic Church. This community was to be guided by Christian values in its politics, economics and social life. Its legal basis was the corpus iuris canonica (body of canon law). The Church's peak of authority over all European Christians in the Middle Ages and common endeavours of the Christian community -- for ...
