GEOMETRY
- geometrical formula
- geometrical comparision and proof
What is realm of mathematical Platonic ideals
The realm of mathematical Platonic ideals, also referred to as Plato's Forms or the World of Forms, is a philosophical concept originating from the works of ancient Greek thinker Plato. It proposes the existence of a separate reality beyond the physical world we perceive through our senses. This realm contains perfect, unchanging versions of all abstract concepts, including mathematical objects like lines, circles, numbers, and even moral concepts like justice or beauty.
Here are some key aspects of the Platonic realm:
Perfect and Unchanging: Unlike the physical world, which is constantly changing and imperfect, the Platonic realm contains perfect and unchanging forms. A perfect circle in the Platonic realm would be a true circle, with no imperfections or variations in its shape.
Independent of the Physical World: The Platonic forms exist independently of the physical world. They are not physical objects themselves but rather the ideal blueprints from which physical objects are derived.
Source of Knowledge: According to Plato, our knowledge of these perfect forms is innate. We are born with an inherent understanding of them, even though we can't directly perceive them in the physical world. This understanding is accessed through reason and contemplation.
Criticisms of the Platonic Realm:
Lack of Evidence: There's no scientific evidence to support the existence of a separate Platonic realm. It relies on philosophical arguments rather than concrete observations.
Duality of Existence: The concept creates a kind of duality, separating the ideal forms from the physical world. This raises questions about how these two realms interact, if at all.
Relevance of the Platonic Realm:
Despite criticisms, the Platonic realm has had a profound influence on Western philosophy and mathematics. Here's why:
Foundations of Mathematics: The idea of perfect mathematical forms provided a foundation for early mathematics. It suggested that mathematical truths exist independently of the physical world.
Conceptual Frameworks: The Platonic realm offers a framework for understanding abstract concepts. It allows us to distinguish between the ideal form (e.g., perfect circle) and the imperfect physical manifestations (e.g., a drawn circle).
In Conclusion:
Whether the Platonic realm exists literally or not, it remains a valuable thought experiment that continues to spark debate and shape our understanding of mathematics, knowledge, and reality.
| Mantrakshar | Hindi | Symbol Name | Meaning / definition | Example |
|---|---|---|---|---|
| ∠ | कोण | angle | formed by two rays | ∠ABC = 30° |
| मापा कोण | measured angle | ABC = 30° | ||
| गोलाकार कोण | spherical angle | AOB = 30° | ||
| ∟ | समकोण | right angle | = 90° | α = 90° |
| ° | अंश | degree | 1 turn = 360° | α = 60° |
| deg | अंश | degree | 1 turn = 360deg | α = 60deg |
| ′ | प्रधान | prime | arcminute, 1° = 60′ | α = 60°59′ |
| ″ | द्वि प्रधान | double prime | arcsecond, 1′ = 60″ | α = 60°59′59″ |
| रेखा | line | infinite line | ||
| AB | रेखा खंड | line segment | line from point A to point B | |
| किरण | ray | line that start from point A | ||
| वृत्त चाप | arc | arc from point A to point B | = 60° | |
| ⊥ | लंब | perpendicular | perpendicular lines (90° angle) | AC ⊥ BC |
| ∥ | समानांतर | parallel | parallel lines | AB ∥ CD |
| ≅ | सर्वगसम | congruent to | equivalence of geometric shapes and size | ∆ABC≅ ∆XYZ |
| ~ | समानता / समरूप | similarity | same shapes, not same size | ∆ABC~ ∆XYZ |
| Δ | त्रिकोण | triangle | triangle shape | ΔABC≅ ΔBCD |
| $$ delim{]}{x-y}{]} $$ | दूरी | distance | distance between points x and y | $$ delim{]}{x-y = 5}{]} $$ |
| π | pi constant | π = 3.141592654… is the ratio between the circumference and diameter of a circle | c = π⋅d = 2⋅π⋅r | |
| rad | radians | radians angle unit | 360° = 2π rad | |
| c | radians | radians angle unit | 360° = 2π c | |
| grad | gradians / gons | grads angle unit | 360° = 400 grad |
Discussion