# Judaism, Christianity, and Geometry

Daniel Alievsky
Translated by Michael Iazovsky

Тraditional symbol of the Jewish faith is the Star of David (Magen David), formed by two mutually superposed equilateral triangles. Traditional symbol of Christianity is the Cross — two straight lines that intercross at right angles.

Let's take a look at these symbols from a purely geometrical point of view. In particular, please pay attention to the corners.

An equilateral triangle has three angles of 60°, constituting of 180°. Respectively, the sum of all six corners of the Star of David is equal to 360°.

The Cross, composed of two ideal mathematical segments, unlike the Star of David, does’t have an internal area and doesn't have interior angles. But these two segments in their intersection form four right angles (90°). And again their sum is 360°.

The simplest geometric object, associating with the magnitude of 360° — it is a circle. The circumference of the circle measured in angular units is 360°. If you take a line and turn it around one of its ends to all of the angles, which are found in the Star of David or in the Cross, the other end of the segment will describe a complete circle.

In most world views the circle symbolizes perfection and wholeness, that in the Jewish tradition is called shlemut. Applying that association to both considered symbols, we will see that shlemut has a common quality of Judaism and Christianity. In other words, both Judaism and Christianity are characterized by completeness and integrity: their followers do not need any other world views, since their own faith has the answers to the fundamental questions of being.

Now let's look at the difference between these two symbols. Corners of the Star of David are the interior angles of triangles, they are exposed to their open part of the center of the configuration. In some sense these six angles actually form the Star of David separating this symbol from the infinite plane around it. In contrast, the Cross angles are external angles and they are exposed outward and cover all the infinite plane that surrounds it.

This association is also evident.

Judaism focuses on the Jewish people, who gather around God in the center of the configuration. According to Jewish Midrash, the shield of King David and his men had just such a form (“Magen David” means “shield of David”). The basic meaning of this symbol is Divine Protection of the Jewish people.

Christianity, in contrast, focuses on humanity around and aims to spread the faith in God to all nations of the world. According to the Christian view, the crucifixion of Jesus was the atoning sacrifice that made it possible to have salvation for all people in the world. Therefore it was exactly the Cross that later became the symbol of the Christianity.

Let's go ahead and calculate the sum of exterior angles of the Star of David, which are formed at the intersection of two lines of triangles facing outwards (as in the case of the cross). There are also six of these angles and each of them is equal to 120°, hence, their sum is 720° = 2⋅360° — i.e. double full circle. It turns out that the attribute of the cross, that it is outward-facing, is inherent also of the Star of David, but in the double degree. The question is what is then the difference of the quality of the Star of David and the Cross, and what is the meaning of a duality? As for me, to my mind comes the following.

The difference is that the exterior angles of the Star of David do not cover the whole plane in general, but the whole plane except for the star itself. In other words, the dialogue of God with the Jewish people is different from the dialogue with other nations, and occurs due to other special rules. Jews are an exception from all the nations, although open to cooperation with the world. Christianity does not exclude itself from the rest of humanity, on the contrary, from a Christian point of view, “there is neither Greek nor Jew.”

The duality can be understood within relation to Christianity. It was that the Jewish people were chosen for the function of “the priests of the world” as early as on the Sinai, where they were obliged to bring the light of Torah to all of 100% of the people of the world. This is the first circle of 360°. Now remember that Christianity was born inside the Jewish nation, but later they realized the dissemination of the light of Torah by an alternative way, different from Hebrew. This is the second circle of 360°. Thus, it appears that the external perfection (shlemut) of the Cross, is the realization of the Divine teachings for all 100% of the people of the world, is a part, or rather, a half of double external perfection of the Star of David.

Does this mean that the Star of David is focused more towards the outside (to work with humanity) than inside (toward closing to the Creator)? No. Two triangles form a regular hexagon at the intersection. Each interior angle of the hexagon is 120° — these angles have common vertices with external angles of the Star, which we counted before. Sum of the interior angles of the hexagon is again 720° = 2⋅360°. Thus, in the Star of David internal and external perfection (shlemut) are balanced on the internal hexagon. The sides of the hexagon are closer to the center than the vertices of the Star. The meaning is quite clear: approach to the center, i.e. to God, doubles the inner perfection.

Just in case I must specify that all the above arguments have purely geometric character and are not intended to set out a theological position. It is possible and likely that the described properties of these geometric symbols of Judaism and Christianity can also admit the other parallels and interpretation.

I express my gratitude to my teacher, rabbi Eli Thalberg, for suggesting the idea of the geometric properties of these two figures.

September 2013

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