Two circles of equal size, each passing through the other's centre, overlap into an almond shape — the vesica piscis. Its height is exactly the width times the square root of three, a provable ratio. Christian art and Gothic architecture later used the shape; what it's said to mean beyond geometry is their own reading.
Why this is hard
The construction is simple: two circles of the same radius, each centred on the other's edge. The lens where they overlap has a height-to-width ratio of the square root of three, a fact fixed by geometry alone. Long after, Christian artists placed figures of Christ inside this shape — the mandorla — and Gothic builders used its proportions in windows and arches.
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Two equal circles make the shape.
Because each circle is centred exactly on the other's edge, by definition.
Two circles drawn through each other, overlapping into a pointed oval.
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The ratio is exactly the square root of three.
Because the geometry of two overlapping equal circles fixes that ratio without exception.
A number that holds true on any two circles drawn this way.
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Christian art placed Christ inside it.
Because artists used the shape, called a mandorla, as a frame for divine figures.
A carved or painted almond, framing a figure meant to be seen as beyond the ordinary.
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Gothic builders used its proportions too.
Because its ratio shows up in window tracery and arch design across Gothic churches.
A pointed arch overhead, built from the same proportion as the shape underfoot.
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Its symbolism is others' reading, not the geometry.
Because what the shape is said to mean was added by artists and mystics after the fact.
The math holding steady, however far the meaning built on it has traveled.
The practice
Draw two circles of the same size, overlapping so each passes through the other's centre. Compare the tall middle shape to its width by eye — noticeably taller than wide. That part is fact. What anyone tells you it means beyond that is a separate claim.
The shape is certain. The meaning is a much later story, layered on after.