 ## 35 Fun Facts about Geometry

The spirit of genuine mathematics, i.e., its methods, concepts, and structure – in contrast with mindless calculations constitutes one of the finest expressions of the human spirit. The great areas of mathematics – algebra, number theory, combinatorics, real and complex analysis, topology, geometry, trigonometry, etc. – have arisen from man’s experience of the world that the infinite, personal, Triune, and Sovereign God has created and currently sustains. These branches of mathematics, constructively developed by man made in the image of God, enable man to systematize the given order and coherence (the unity in diversity … the proximate one and the many) of creation mediated to us by the Creator and upholder of all things – the logos and wisdom of God revealed in the person of the Lord Jesus Christ. This systematization not only gives man a tool whereby he can take effective dominion over the creation under God in Christ, but also gives man the experience and enjoyment of a rich intellectual beauty that borders the sublime in its infinitely complex, yet structured mosaic.
James Nickel

Geometry is a fascinating branch of mathematics that has captivated mathematicians for centuries, exploring the shapes, sizes, and relative positions of objects. Yet, in our daily lives, we often come across numerous geometric shapes without giving much thought to their mathematical significance.

Take pizza, for instance, which is typically round, served in a square box, and sliced into triangular pieces. The geometry behind this is intriguing, and in this blog post, we will delve into 35 such wonders of geometry that surround us in everyday life.

Geometry, derived from the Greek (γεωμετρία) word Geometron, is the study of the properties and relationships of points, lines, shapes, and spaces. The term geo refers to Earth, while metron means measurement.

The maximum number of intersection points between two distinct lines is one because two distinct lines must intersect at exactly one point, or they may not intersect at all.

The sum of the internal angles of a triangle is equal to 180 degrees. This property is known as the angle sum property of a triangle.

A standard football (also known as a soccer ball) is made up of 32 panels, which are usually hexagons and pentagons. Specifically, there are 12 pentagons and 20 hexagons on a standard football.

The sum of the opposite faces of a die is always 7. For instance, if one side shows 6 dots, the opposite side will show 1 dot, and their sum will always be 7.

The centre of a circle is unique, and in order to determine a unique circle, we need at least three non-collinear points.

Did you ever notice that the cells inside beehives are hexagonal? Interestingly, each wax cell may vary slightly in size, but they are all alike in their basic shape, which is a hexagon. This shape is a distinctive feature of a honeycomb, which is created by bees to store their larvae, honey, and pollen.

The sum of the internal angles of a quadrilateral is equal to 360 degrees. This property is known as the angle sum property of a quadrilateral.

Note. The sum of interior angles for an n-sided polygon is (n – 2) × 180º.

The Seven Bridges of Königsberg is a famous problem named after the city of Königsberg, which was connected to two large islands by seven bridges. The problem, first posed in 1736 by Leonhard Euler, asked whether it was possible to find a walk through the city that would cross each bridge exactly once and end at the starting point. Euler proved that such a walk was impossible, laying the foundation for the modern field of graph theory.

The ratio of the distance between the fingertip and the elbow to the distance between the elbow and the wrist is often cited as being approximately equal to the golden ratio ф (phi), which is approximately 1.618.

This formula is named after the mathematician Leonhard Euler, who first discovered it in the 18th century. In any convex polyhedron (a three-dimensional solid with flat polygonal faces), the number of its vertices (V), edges (E), and faces (F) are related by the equation:

VE + F = 2.

Cutting a sandwich diagonally to form two triangular halves is traditionally more common than cutting it into two rectangular halves. There is no definitive answer to why sandwiches are traditionally cut diagonally, but there are several possible reasons. Firstly, cutting a sandwich in half diagonally makes it easier to handle and eat. Secondly, a sandwich that is cut diagonally is often perceived as more visually appealing than one that is cut straight across. Lastly, the diagonal cut can create the illusion that the sandwich is bigger, which may make it more appealing to eat.

The Exterior Angle Sum Theorem in geometry states that the sum of the exterior angles of a polygon is always equal to 360 degrees. Regardless of whether the polygon is a triangle, quadrilateral, hexagon, or decagon, the sum of its exterior angles remains constant.

Eggs cannot be classified as circular or elliptical in shape, as they possess an oval shape. Specifically, chicken eggs are a prime example of ovals. If you observe an egg closely, the distance from the centre is not a fixed circle. The horizontal aspect has a longer ellipse-like form. Observing closely once again, one horizontal direction is roundly curved but the other is pointed. This is the shape of an egg.

Given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity that starts at A and reaches B in the shortest time? This classical problem is known as the Brachistochrone problem, which was posed and solved by Bernoulli in 1696. The curve of fastest descent is not a straight line or a polygonal line but a cycloid.

The ratio of the circumference of any circle to its diameter is a constant value known as pi (π), which is approximately equal to 3.14. Pi is an irrational number. Pi Day is celebrated on March 14th (3/14), which is a reference to the first three digits of pi.

Potato chips come in various shapes and sizes, but Pringles are unique due to their saddle shape, which is a hyperbolic paraboloid. This shape was chosen because it allows for uniform stacking of the chips in the canister, maximizing storage space while minimizing breakage. Furthermore, the saddle shape ensures that each chip is evenly cooked during the manufacturing process, resulting in consistent flavor and texture.

When two straight lines are cut by a transversal, the corresponding angles are formed on the same sides of the transversal and the alternate angles are formed on opposite sides of the transversal.

Mathematicians have determined that there are only 17 distinct types of planar symmetry that can occur in a repeating wallpaper pattern.  However, it’s important to note that within each of these 17 groups, there are many possible variations in terms of colour, texture, and other decorative elements.

We can hold more sand if we make a cylinder with a smaller height and a larger radius compared to a cylinder with a bigger height and a smaller radius using an A4 size paper.

Typical ceiling fans have three blades, each inclined to the adjacent at an angle of 120°. The 3 blades are positioned at equal angles so that the net force they apply becomes 0 and there isn’t any force remainder in any direction.

Ice cream holders are looked like hollow thin walled circular base cones or sometimes frustum of a right circular cone (prepared from wheat and corn flour). The purpose is to efficiently hold the ice cream. If the scooped balls of ice cream can be approximated as spheres, then a cone will hold the most amount of delicious ice cream and the least amount of air.

There are 43252003274489856000 possible configurations of the Rubik’s Cube. Every Rubik’s Cube configuration can be solved in 20 moves or less. This is known as God’s Number. The 3 × 3 × 3  Rubik’s Cube contains 26 unique miniature cubes, also known as cubies (or cubelets).

The hour and minute hands of a clock are perpendicular to each other 44 times in a day.

1 radian is more than 1 degree. In fact, 1 radian is approximately equal to 57.2958º.

The Hanging Chain problem is a classic problem in mathematics that involves finding the shape of a hanging chain suspended between two points under the influence of gravity. The solution is given by the catenary, which is a curve with a shape similar to a parabola but wider and flatter, and provides a stable equilibrium for the hanging chain.

The main supporting structure for overhead electric transmission lines is the towers. Transmission towers are designed to bear the weight of heavy transmission cables and elevate them above the ground. Triangular shapes are often used in structures such as electric towers (known as cross arms) because they are rigid and stable. A triangle’s shape distributes forces evenly, making it stronger and more resistant to bending or breaking compared to a quadrilateral. Additionally, triangular structures use less material to achieve the same level of stability, which makes them more cost-effective to build.

Metatron’s Cube connects thirteen circles in the Fruit of Life shape with straight lines and contains all five Platonic Solids, representing universal geometric patterns.

If a ball is projected at an angle of 45 degrees with respect to the horizontal, it will travel the maximum distance possible.

To divide a given figure into eight pieces, a minimum of three cuts are required. These three cuts must be made horizontally, vertically, and by the base.

The international paper sizes such as A3, A4, and others, are based on the square root of 2. The dimensions of an A4 size paper are 210 mm × 297 mm, and that of an A3 size paper is 297 mm × 420 mm. If we assume that the height is greater than the width, then the ratio of the height to the width of all formats is √2 or 1.414. Joining two A4 size papers will result in one A3 size paper, two A3 size papers will give you one A2 size paper, and so on.

An asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. The word derived from the Greek ἀσύμπτωτος. There are three kinds of asymptotes: horizontal, vertical and oblique.

A platonic solid is a 3D shape where each face is the same as a regular polygon and has the same number of faces meeting at each vertex. There are only five Platonic solids and they are tetrahedron, cube, octahedron, dodecahedron, and icosahedron. They were first discovered by the ancient Greek philosopher Plato, who believed that they represented the five elements of the universe: earth, air, fire, water, and ether.

If two straight lines are neither parallel nor intersecting, they are called skew lines in three-dimensional geometry. Two lines are skew if and only if they are not coplanar. Since two lines in the plane must intersect or be parallel, skew lines can exist only in three or more dimensions.

Normally pizza is round, has a square box for delivery but is cut into triangles. Pizzas are mostly circular as it allows for even cooking and heat distribution in a round oven, resulting in a delicious and evenly-cooked pizza. Square pizza boxes are more practical and economical as they fit neatly, stack easily, and take up less space than circular boxes during transport. They are also easier and less expensive to produce. Cutting pizza into triangular slices is practical and convenient, as it ensures equal portions of toppings and crust, maximizes the number of slices, and allows for easy sharing and portion control.

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