Real Life Examples of Geometry Quiz

Answer: Hexagon

To tessellate means to tile a plane completely, without leaving any gaps in between. The three options are the only polygons that can fully accomplish this. But, of all three, hexagons cover the most area for the same perimeter, making them more efficient in terms of space. Moreover, in the case of beehives, the hexagonal structure holds more weight with less amount of material.

As a matter of fact, the cells in a beehive are not perfectly hexagonal. Bees actually build them with a circular shape, but the body temperature softens the wax and it turns into a somewhat hexagonal tube as it re-solidifies.

Answer: Rugby

The formal definition of a sphere is the set of points in a three-dimensional space that are equidistant of another fixed point, called the center, (with the distance being the radius). As all the points are located at the same distance away from the center, the result is a shape that has no corners and no edges at all.

Sports balls, however, are not technically perfect spheres, since they have certain features that don't comply with the formal definition of a sphere (like the dimples on the golf ball, the seams on the tennis ball, the stitches of the volley ball), but they are pretty much round in shape, having the general look of a spherical object.

A rugby ball, on the contrary, is more oval-like (the technical term would be "elongated prolate spheroid").

Answer: Tetrahedron

Being a polyhedron with four faces, the word we're looking for is tetrahedron (from Greek "tetra", meaning four, and "hedros" meaning sides or faces).

There are a few interesting facts about the tetrahedron. One of them is that, in a regular one (where all the faces have the same area), all of its vertices are equidistant from each other, being the only possible arrangement of four equidistant points in a three-dimensional space. Plus, it is the only one among the uniform polyhedra that has no parallel faces.

In case you were wondering, the Great Pyramid of Giza is actually NOT a tetrahedron. A pyramidal tetrahedron only has three of its faces "exposed", while the fourth one acts as its base. Egypt's pyramid has actually FOUR exposed triangular faces, and rests atop a fifth one which would be square, making it an irregular pentahedron.

Answer: Octahedron

As you can see, Ether's logo consists of two pyramidal pentahedrons "facing" each other. As one face from each would be "cancelled" if they'd join together, that would leave four exposed faces from each one, totalling eight. Hence, it would be a octahedron.

As to whether it is a regular octahedron or not, the condition a polyhedron must satisfy to be regular is that all of its faces, edges, and angles must be equal, which, in this case, could only happen if all the exposed faces were shaped as equilateral triangles.

Answer: Sinuosity

The sinuosity of a continual dfferentiable curve can be defined as the ratio of the length of the actual curve and the straight line distance connecting both ends of the curve. The values can range from 1 (a straight line) to infinity (a closed loop).

The term "sinuosity" is derived from the sine trigonometric function - not because of the definition of the function, but rather because of its graphical representation, which is also a meandering curve.

Answer: Arc

In simple terms, a parabola is a set of points that have the characteristic of being at the same distance from a fixed point (focus) and a straight line (directrix). The focus is located inside the parabola, while the directrix is on the outside, "behind" it. The vertex is the extreme point of the parabola, the place where it changes direction. While the parabola is somewhat shaped like an arc, that's not one of the constituent elements of it - what mainly defines a parabola are the focus and the directrix.

A very useful property of parabolas is that if any kind of wave, (be it light, sound, etc.) traveling parallel to the parabola's axis of symmetry, hits the concave side of it, the wave will be reflected directly towards the focus. This is what makes the parabola very useful in several daily objects, like the parabolic antenna shown in the picture, or the headlights of a car, for instance.

Answer: Pentagon

The five-sided polygon (pentagon) has a very particular property: in a regular pentagon, the relation between the length of any of its diagonals and the length of any of its sides, is equal to the Golden Ratio (1.618034 approx.), which has been considered a measure of harmony and aesthetic proportion in many fields of study. Hence, Ancient Greeks, for example, revered the shape of the pentagon for its aesthetic proportion, while Ancient Chinese used it as a symbolism of the five elements of nature.

Since the building of the Pentagon, the headquarters of the US Department of Defense, the shape has been considered a symbol of power and strength.

By projecting each of the sides of a regular pentagon away from the shape's outline, up to the point where they intersect each other, you'll obtain another highly symbolic shape, the pentagram, or five-pointed star. The pentagon is also seen in a regular dodecahedron, as each of its faces is shaped like a regular pentagon.

Answer: Octagon

Road signs come in many shapes, more commonly circles, triangles and squares. However, the "Stop" sign, in several countries, comes in an octagonal shape, with no other sign shaped like that. The reason for it is that, being a peculiar shape, it's easily recognizable for drivers even at a distance, making it easier for them to react to it on time. In some countries, though, the sign is circular.

As its name implies, an octagon is a polygon with eight sides. In a regular octagon, such as the one in the sign, the internal angles have a magnitude of 135° each, with all of them adding up to 1080°.

Of the wrong choices, heptagon is seven-sided, hendecagon (or undecagon) is eleven-sided, and pentadecagon is fifteen-sided.

Answer: Nonagon

A nine sided polygon, like the one shown in the picture, is commonly known as "nonagon". The name is not really correct in terms of etymology, as it is a mixture of a Latin prefix ("nonus", ninth) and a Greek suffix ("gonon", corner or angle). A more precise name would be "enneagon", but it's rarely used.

Being an odd-sided polygon, a nonagon does not have axial symmetry, but it does have rotational and reflective symmetries. Its area can be calculated with the formula (9/4) * s^2 * cot(pi/9), with "s" being the length of one side, and "cot" being the cotangent function.

It is not common to see practical uses of a nonagon, but it does have its applications, particularly in architecture. A notable example is the Baha'i Houses of Worship, which are required to be nonagonal.

For the record, the wrong options are made-up words, based on the number nine written in French ("neuf"), Portuguese ("nove") and Swedish ("nio").

Answer: 20

Being a twenty-faced polyhedron, there are pretty much infinite kinds of it, depending on the size and shape of their faces.

The common regular icosahedron consists of twenty equilateral triangles as its sides, with its vertex figure (the shape you see when looking straight in front of one vertex) being a pentagon. However, there is another regular type, called the "great icosahedron". What distinguishes it from the regular type is that the triangles that make its faces intersect each other, giving it a vertex figure of a pentagram.