# Geometrical Curiosity – Tilted Equilateral Triangle, The Square & Compasses

## A Tilted Equilateral Triangle…

…is produced using the three primary shapes of geometry: a circle, an equilateral triangle and a square.

**The design of a tilted equilateral triangle is a geometric curiosity, in that ‘the properties of 2 of the 3 shapes listed can produce the perfect form of the third’.**

For example: starting with a square, an internal square could be added and twisted at 45°. Inside the inner square a circle could be drawn.

Taking any corner of the larger square and projecting two lines out so that they touch the circumference of the inner circle, this produces an angle of 60°. Then, using the side of the tilted square that was opposite to the former corner, the extension of that side intersects with the two previously projected lines to produce a perfect equilateral triangle; set at 45°.

An added curiosity is the fact that **the exact centre of each shape is at precisely the same point **as each other’s.

Due to this, those who believed that geometry was the building block of life and/or creation (sacred geometry) saw this as the perfect presentation of the Trinity, either in an ancient form or in the Christian form; each shape is independent, but is also the sum of the other two.

As you can see in this image, the base of the Triangle is tilted at 45′.

If you also look at this pentacle, you will see that when an Equilateral Triangle is placed in a specific way so that two of the triangle’s corners sit over two points of the star, the resulting Tilted Equilateral Triangle is also tilted at the same angle as above, 45′.

The Tilted Equilateral Triangle can also be constructed using the fundamental device of Sacred Geometry, the vesica piscis…

**Possible Blueprint for the Freemason’s Established Logo**

Some researchers have suggested that the Freemason’s logo which consists of a **Square & Compasses** is simply a corrupted version of the Star of David or the Seal of Solomon, but as you can clearly see in the animation which I have created, the established logo of the **Freemasons** is cleverly laid over the top of a Tilted Equilateral Triangle, albeit off set by 45’…

Does anybody know whether or not the concealment of the Tilted Equilateral Triangle within the design of the masonic Square & Compasses symbol is purposeful or accidental?

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