We don’t know when the prehistoric man started using natural numbers (1, 2, 3, …) for counting. This was undoubtedly a major intellectual achievement, and the first stage of mathematical abstraction: the concept “three” is a familiar abstraction of 3 sheep or 3 apples, etc. In addition to being used for counting, natural numbers can be used for ordering (as ordinal numbers: first, second, third, …). Once the base units are introduced they can also be used for measurements (e.g., for time: one year, two years, three years…). No one can underestimate the importance of this discovery for ancient civilizations. You cannot leave the exhibition without being amazed by Fibonacci with his sequences and exhausted by Sissa Ben Dahir from counting, as he exhausted the King of India before you when he asked for wheat instead of gold for his invention of chess.
Numbers

1) History of Numbers
Sounds, languages, signs, letters and numbers are one of the creations and needs of man in any society and civilization, and between man and these tools there is a close and eternal connection and links; because sounds, languages, actions, signs, movements, sensations, letters and numbers are tools of perception, understanding and communication between people to achieve private and public goals, and between people and other creatures. Therefore, every language must include what the community needs in terms of words and meanings indicating everything – including numbers and figures – for reasons that prevailed in the isolation, separation and self-reliance of each community, and for other reasons such as fear and infighting. But circumstances, life, and the environment have changed, and small and weak societies have begun to die out, and societies, civilizations, and continents have merged and will continue to merge. Many specificities, societies, and civilizations have disappeared and will disappear; such as cuneiform, pharaonic and Latin numbers, some of which are still in use. There are many other numbers, letters, languages, writings and cultures that have become confined to books and references, after they were once bright and active and replaced others. This includes some numbers and mathematical methods that are no longer known to us in any way for reasons such as:
1) The lack of usefulness and feasibility of such numbers and calculations, which caused their disappearance and extinction.
2) The extinction of the people and nations of these numbers and accounts.
3) The convergence and coexistence of human societies led to the overlapping and merging of the main tools of understanding such as:
- Languages.
- Letters.
- Numbers… etc.

2) Are You a Square? (Proportionality in the Human Body)
Compare your proportions to classic ideas. This painting is by Leonardo da Vinci (based on Vitruvius’ book) and shows a “classical” figure with a ratio of height to arm span.
Is your ratio close to 1?

3) Exponentiation of 2 and exponential growth
In modern computer science, the complexity of a task is measured by the amount of time it takes (depending on the number of binary digits entered). Task time can be linearly (or polynomially) or exponentially proportional to the size of the input. Linear (or polynomial) growth means that the time is proportional to the size of the input (or a specific exponent of it). Exponential growth means that with each new binary digit entered, the task time becomes multiplied by a fixed quantity, such as a multiple. This shows that exponential growth precedes polynomial growth. Therefore, polynomial time algorithms are more efficient than exponential time algorithms.

4) Mind the Road Functions
Describing the world mathematically is based on the concept of functions. The temperature on a mountain depends on altitude, and the distance from Naples depends on time. Of course, mountains in different climate zones, or different journeys from Naples to Rome, will be described by different functions.
Functions are usually represented by a graph in a plane. On the horizontal axis (x) is the “independent variable” (altitude, or time) and on the vertical axis (y) is the “dependent variable” (temperature, location). At any given altitude or time (to the right of the vertical axis), the graph shows the temperature or location (above the horizontal axis).

5) Golden Ratio and Fibonacci Sequence
In mathematics, two numerical values realize the golden ratio if the ratio between the sum of these two numbers and the largest of them is equal to the ratio between the largest and the smallest of them. It is a defined mathematical constant with a value of approximately 1.6180339887.
For example, in the golden rectangle.