Geometry

In Deals and Maths

A rhombus can also be referred to as a diamond, especially in everyday language due to its diamond-like shape. In more technical terms, it is sometimes called an equilateral quadrilateral because all four of its sides are of equal length. Additionally, it can be classified as a parallelogram since it has opposite sides that are parallel.

Two methods ;-

#1 ; Use Pythagoras, if the lengths of the other two sides are known.

h^(2) = s(1)&(2) + s(2)^(2)

In words, 'The hypotenuse squared is the sum of the squares of the other two sides.

#2 ; Use Trigonometry (trig.) is the length of one side and an angle are known .

Hence

Sin(angle) = opposite / hypotenuse

hypotenuse = opposite / Sin(angle)

or

Cos(angle) = adjacent/hypotenuse

hypotenuse = adjacent/Cos(angle).

A cylinder has an infinite number of axes of symmetry. Any axis that passes through the center and is perpendicular to the circular bases serves as an axis of symmetry. Additionally, any vertical axis that passes through the center of the cylinder's height and intersects the circular bases also acts as an axis of symmetry.

An octagonal prism consists of two octagonal bases and eight rectangular lateral faces. Each of the rectangular faces is a parallelogram, as all rectangles are special cases of parallelograms. Therefore, in addition to the two octagonal bases, there are eight parallelograms (the rectangular lateral faces), making a total of ten parallelograms in an octagonal prism.

When comparing the two cylinders with given values of radius (r) and height (h), one can observe how the ratio of height to radius affects their proportions. If the ratios are similar (e.g., both cylinders have the same height-to-radius ratio), they will appear proportionally identical, even if their absolute dimensions differ. Conversely, differing ratios will lead to distinct shapes, with one cylinder appearing taller or shorter in relation to its width. Overall, the relationship between r and h is crucial in determining the visual proportion of the cylinders.

The symbol with a cross and a circle at the bottom is commonly recognized as the astrological symbol for Venus, representing the planet and the goddess of love and beauty in Roman mythology. In various contexts, it can also symbolize femininity or the female gender. Additionally, it is used in alchemy to denote copper.

A regular doodle star typically has angles that vary based on its design, but if we consider a simple five-pointed star, the internal angles at the tips of the star are each 36 degrees. The angles between the points (the inward angles) can vary depending on how the star is drawn, but they often measure around 108 degrees. The exact measurements can differ based on the specific style and proportions of the doodle star.

Mo such shape/thing as a 'polgon'.

If you mean ' polygon'.

The word 'polygon' means a 2-dimensional shape (--gon) of many sides (poly--).

So the word 'polygon' mean an many sided shape.

For a specific number of sides it becomes;-

trigon ( triangle) 3 sides

quadragon ( quadrilateral ) 4 sides

pentagon 5 sides

et seq.,

Three sides. They are

Obverse ( Front)

Reverse ( Back)

Rim ( rounded edge).

When a plane intersects both nappes of a right circular cone without passing through the vertex, the resulting curve is a hyperbola. This occurs because the plane cuts through both sides of the cone, creating two separate branches of the hyperbola. The precise shape and orientation of the hyperbola depend on the angle at which the plane intersects the cone.

To find the lateral surface area of a pyramid, calculate the area of each triangular face and sum them up. For a regular pyramid, this can be done using the formula ( \text{Lateral Surface Area} = \frac{1}{2} \times \text{Perimeter of the base} \times \text{Slant height} ). The total surface area is then found by adding the area of the base to the lateral surface area: ( \text{Total Surface Area} = \text{Lateral Surface Area} + \text{Area of the base} ).

Yes, a precision approach can be circled off if the pilot determines that they cannot safely land on the intended runway. This decision is typically made when there are unfavorable weather conditions, obstacles, or other hazards that compromise safety. The pilot would execute a go-around and maneuver the aircraft to enter a different traffic pattern or approach to another runway if necessary. It's crucial for pilots to prioritize safety and follow established procedures during such situations.

The vertical distance between two points refers to the difference in their vertical coordinates, typically measured along the y-axis in a Cartesian coordinate system. This distance can be calculated by subtracting the y-coordinate of one point from the y-coordinate of the other. It is often used in various applications, such as geometry, physics, and engineering, to determine elevation changes or heights.

The combination of sizes of shapes and grains refers to the diversity in the dimensions and forms of particles or materials within a specific sample. This variation can influence properties such as texture, strength, and flow behavior in materials like soils, sediments, or granular substances. Analyzing these combinations helps in understanding how materials interact and perform in various applications, from construction to filtration.

The cable cross section for a 150 kVA load depends on several factors, including the voltage level, installation method, ambient temperature, and allowable voltage drop. Generally, for a three-phase system at 400V, a cable size of around 35 to 50 mm² is commonly used, but this can vary. It's essential to consult the relevant electrical standards and perform calculations based on specific installation conditions to ensure safety and compliance. Always consider seeking advice from a qualified electrical engineer for precise sizing.

Sin(Sine) is a cyclic curve.

This cyclic curve(wave) that repeats every 360 degrees ( or 2pi radian).

Its Amplitude ranges from (+)1 to (-)1

When learning about trigonometry(Trig.) you only learn the bit between 0 degrees and 90 degrees.

On extending this learning you will find it to be a cyclic curve.

The word 'Sine'(Sin) is from Latin and means 'curve'.

The word 'Cosine(Cos) means 'complimentary sine' . It is the same curve as Sine but shifted along the x-axis by 90 degrees.

The Ratios is

Sin(angle) = opposite/ hypotenuse.

A major arc is a portion of a circle that is greater than 180 degrees. Its measure is calculated as the difference between 360 degrees and the measure of the corresponding minor arc. Therefore, if a minor arc measures, for example, 120 degrees, the major arc would measure 240 degrees. In summary, a major arc's measure is always greater than 180 degrees and less than 360 degrees.

Polygons with 21 to 100 sides are named using a combination of Greek or Latin prefixes and the suffix "-gon." For example, a polygon with 21 sides is called a "icosagon," while a 22-sided polygon is a "dicosagon." This naming convention continues up to 100 sides, where a polygon with 100 sides is known as a "hectogon." Each name typically combines the prefix indicating the number of sides with the "-gon" suffix.

A regular star, specifically a five-pointed star (pentagram), has 10 lines of symmetry. Each line of symmetry can be drawn through a vertex and the midpoint of the opposite side or through the midpoints of two opposite points. For stars with more points, such as a six-pointed star, the number of lines of symmetry would vary accordingly.

In a regular polygon with 5 sides (a pentagon), each interior angle can be calculated using the formula ((n - 2) \times 180^\circ / n), where (n) is the number of sides. Substituting (n = 5), we get ((5 - 2) \times 180^\circ / 5 = 108^\circ). Therefore, each interior angle in a regular pentagon measures 108 degrees.

The two angles described are known as adjacent angles. They share a common vertex and one side, while the other sides of the angles are formed by extending the common side in different directions. Since they do not overlap, adjacent angles can be found in various geometric configurations, such as in polygons or when two lines intersect.

A mexagon is a geometric shape with six sides and six angles, similar to a hexagon. Each side is typically of equal length, and the angles are generally equal as well, making it a regular polygon. Visually, it appears like a flat, two-dimensional figure with a symmetrical, rounded appearance. The term "mexagon" is less common than "hexagon," but it represents the same shape.

NO!!!!

The 'hypotenuse' only refers to the longest side of a Right-Angled triangle.