**HORIZON**

Exploring the visual and mathematical horizon – paintings by Tina Mammoser

*October – November 2015
*

The main feature in most of my paintings is, of course, the horizon line. Where water meets sky.

But how far away is the horizon? It’s all in the math of a circle – and the circle is the Earth. Read below the images for more info!

**Frinton Blues**

Acrylic painting on canvas

70x60cm

£1000

**Brightlingsea**

Acrylic painting on canvas

70x60cm

£1000

**Rise Up**

Acrylic painting on canvas

60x50cm

£900

**Naze Autumn**

Acrylic painting on canvas

60x60cm

£900

;

**New Year Night**

Acrylic painting on canvas

80x80cm

£1600

A triangle is formed by our height, the radius of the earth and the distance before the curvature of the Earth starts to bend away from us.

The three sides of the triangle are:

- A. The horizon: distance from viewer to where it meets the curve of the Earth. (Where a line meets the edge of a circle it always makes a right angle, 90 degrees, with the line that is the radius of that circle. That line is called a tangent.)
- B. The Earth radius is the base of the triangle.
- C. The Earth radius plus our height is the longest side of the triangle (the hypotenuse).

Using the Pythagorean Theorum for a right triangle:

A^{2} + B^{2} = C^{2}

(Horizon) ^{2} + (R) ^{2} = (R + Height) ^{2}

For example let’s take a very tall person: 2m tall. (about 6’5″)

Then:

(Horizon) ^{2} = (6,378,000m + 2m) ^{2} – (6,378,000m) ^{2}

(Horizon) ^{2} = (6,378,002m) ^{2} – (6,378,000m) ^{2}

Multiply this out to get:

(Horizon) ^{2} = 25,512,004 m^{2}

Horizon = square root of 25,512,004 m^{2}

Horizon = 5050.94m

Horizon = 5.05km = 3.14 miles

Plus, due to refraction of light – the way lightwaves bend in the air due to the density of our atmosphere – we can actually see a little farther. Spookily, our vision goes slightly AROUND the bend of the Earth.