Understanding 10 Key Principles of Graphic Representation
Principle of Multiple Application
This patterning process involves the use of a simple figure to represent a variety of objects and body parts. With a limited graphic vocabulary, an artist can represent very different things. This process is useful for its economy of means and communicative effectiveness.
Principle of the Baseline
The baseline is a horizontal line that crosses the drawing near the bottom, serving as the support for characters, animals, plants, and objects. It is a very useful graphical
Read MoreEssential Business Math and Financial Formulas
1. Average Calculation Formula
Formula: Average = (Sum of all values) / (Number of values)
Example: Find the average of 10, 15, 20, 25, 30
- Sum = 10 + 15 + 20 + 25 + 30 = 100
- Number of values = 5
- Average = 100 / 5 = 20
2. Ratio and Proportion Formulas
Ratio: a:b = a/b
Proportion: If a:b = c:d, then a/b = c/d or ad = bc
Example: If 3:4 = x:12, find x
- 3/4 = x/12
- 3 × 12 = 4 × x
- 36 = 4x
- x = 9
3. Percentage Formulas
Basic Percentage: Percentage = (Part / Whole) × 100
Percentage Increase/Decrease: ((New Value – Old
Read MoreFundamental Numerical Methods and Error Analysis
1. Error and Its Types
Errors in numerical methods occur due to approximations, limitations in computations, and human mistakes. They can be classified as:
A. Inherent Error
This error naturally exists in the problem itself, independent of numerical methods used to solve it. It arises when the exact value of a quantity is unknown or impossible to determine.
Example:
The value of π\pi is an infinite decimal (3.1415926535…). If we approximate it as 3.14, we introduce an inherent error.
B. Numerical Error
These
Read MoreProbability Simulations and Statistical Analysis using R Programming
Repeat 1000 times the experiment you performed in Task 1, that is rolling a tetrahedron die 10 times and computing the average. Report the average and standard deviation of the 1000 experiments. The standard deviation function in R is sd(x).
S = 1000
rolls.Avgs = vector(length = S)
for(simnum in 1:S){
x = 1:4
roll = sample(x, 10, replace = TRUE)
rolls.Avgs[simnum] = mean(roll)
}
mean(rolls.Avgs)
sd(rolls.Avgs)
# compute the mean of the 1000 experiments
mean(rolls.Avgs)
hist(rolls.Avgs, main=””, xlab=
Essential Geometry Terms and Definitions Glossary
A
Acute Angle
An angle measuring less than 90°.
Acute Triangle
A triangle where all three interior angles are acute (less than 90°).
Altitude of a Triangle
A perpendicular segment from a vertex to the opposite side or to a line containing the opposite side.
Angle
It is formed by two rays that share a common endpoint, provided that the two rays are noncollinear.
Angle Bisector
A ray that contains the vertex and divides the angle into two congruent angles.
Arc
Two points on the circle and a continuous part
Read MoreEssential Geometry Concepts: Formulas, Proofs, and Theorems
Fundamentals of Geometry
Undefined Terms and Basic Figures
- Point: Exact location in space with no size, written as a capital letter (e.g., A).
- Line: Straight path extending infinitely in both directions, no thickness, named with two points ($\overleftrightarrow{AB}$) or a lowercase script letter.
- Plane: Flat surface extending infinitely in all directions, named with a script capital letter or three non-collinear points.
- Collinear Points: Points that lie on the same line.
- Coplanar Points: Points that lie