Some geometrical data and formulas that can be very handsome
b: (small) width
d: (small) diagonal
h: height
l: length
s: hypotenuse
r: radius, distance between the center and circumference of a circle
z: side
π: 3,1416..
|
shape |
description |
perimeter |
surface |
|
circle |
perfect ring around one center |
2 x π x r |
π x r x r |
|
ellipse |
oval with two centers |
short radius a x long radius b x π |
approximately π√2(a2+b2) |
|
square |
4 equal sides and angles |
4 x z |
z x z (of z2) |
|
rhombus |
opposite corners and four sides equal |
4 x z |
(D x d)/2 |
|
rectangle |
4 right angles |
2 x (l + b) |
l x b |
|
parallellogram |
2 x 2 parallel sides |
2 x (b + s) |
b x h |
|
triangle |
3 corners together 180 |
z + z + z |
(b + h)/2 |
|
trapezium |
truncated triangle |
z + z + z + z |
(B+b) xh / 2 |
|
form |
definition |
area |
content |
|
globe |
ball |
4 x π x r |
4/3x π x r3 |
|
cilinder |
tube |
2 x π x r x h |
π x r2 x h |
|
spherical part |
round cap |
π x (rn2 + h2) |
1/6 πh(3 rn2 + h2) |
|
cuboid |
cuboid |
l x b x h |
|
|
pyramid and cone |
point |
1/3h x ground surface |
|
Pythagorean Theorem
If triangle ABC has a right angle at C, then a2 + b2 = c2
The formula is often called the 3-4-5 rule and is used to make a right angle:
32 + 42 = 52, or:9 + 16 = 25 (centimeters, meters,...). Take a side (rope) of 3 meters, one of four meters and connect them with a 5-meter: this provides a perfect right angle of 90°.
Rope with 13 knots
In the Middle Ages, this tool wasn’t lacking in any yard. By emphasizing 13 knots at the same distance from each other in a rope that was suitable to make a circle and to create an equilateral triangle, but also a right triangle, and therefore also a square and a cuboid.
It was also a calculation tool to add, in a simple way numbers; subtract, multiply and divide as well. For large numbers, a rope with more knots wase used.
The Celsius - and Fahrenheit scale
18° F = 100°C or 1°C = 1.8° F
formula for conversion from°C to F°
x°C = (9/5x + 32)° F
formula for converting° F to°C
x° F = (x - 32) 5/9°C
Surface units
1 are = 10 x 10 = 100 m²
1 hectare (acre) = 100 are = 10,000 m2 ex. 100 x 100 m (hecto means 100)
centiares = 1 m²
roe (the): there are many large regional differences: from 11, over 13, 16, 30 and 33m ²
There are other regional terms and sizes, but which are in fact not universally applicable.
Pi (π, from the Greek perifereia or circumference) is the constant which is the ratio between the circumference of a circle and the cross-section. The circumference of a wheel is 3.14159 times its diameter (from edge to edge over center). That number, we need (for example) in order to calculate the area of a disc.
Archimedes devised an ingenious solution to calculate the area of a circle. Draw a square in it, and one around it. The difference between the two surfaces approaches that of the disk. If you have instead of a square a 5 - angle, 6 -, 9... - angle, the calculation is more and more accurately. He went to a 96 angle. A short time later, the Chinese Liu Hui went to a 3,072 angle. Today there are computers (with different algorithms) that calculate pi still more accurate.
To remember a series of digits of pi, there are several rhymes sought, in which the number of letters of a word stand for each digit. (Only after 31 decimal places there will be a zero.)
How I wish I could calculate pi
or
Sir, I bear a rhyme excelling
In mystic force, and magic spelling
Celestial sprites elucidate
All my own striving can't relate
Or locate they who can cogitate
And so finally terminate. Finis.
A constant is a fixed, unchangeable quantity or value.
The speed of light (or other electromagnetic radiation in a vacuum):
c = 299 792 458 m / s or completed 300 000 kilometers per second.
The standard meter is the distance traveled by light in 1/299 792 458 seconds.
In air, this value is 0.03% lower.
OK, so what's the speed of dark?
The speed of sound is dependent on factors such as temperature and humidity.
For air at room temperature (20°C) is the rate approximately 343 meters per second or 1,234.8 km / h.
When dry air (with little water vapor) at 0°C is that 331 m / s or 1,194 km / h.
In liquids and solids is the speed of sound usually higher. In water it is about 1,500 m / s, and in wood approximately 3,300 m / s, in steel about 5,800 m / s. In the hardest metal sound speed can be up to 12,000 m / s.
Gravity, gravity field strength (or gravitational field strength) is the strength of the gravitational field and is for the earth called the acceleration of gravity g. It is the speed with which objects are in free fall to the earth, without influence from other forces.
On the surface, the gravity average is approximately 9.81 m/s2. So the speed of an object in free fall (in vacuum) will increase with every second about 9.81 m / s. After 1 second, it has a speed of 9.81 m / s, and after 2 seconds, 19,62 m / s and so forth.
But you have to take into account air resistance.
Location- values : 9.780 m/s2 equator; pole 9,832 m/s2, Benelux 9,812 m/s2.
The speed of sound is 100 meters per second, Sundays, however, 150. (Paul Rodenko)
Nothing travels faster than light except bad news. (nr Douglas Adams)