Mathematics in architecture
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Indian architecture followed principles of vastu shastra, aligning buildings with cosmic movements. Cities like Harappa and Mohenjo-Daro were precisely planned using mathematical drawings. Jaipur's design was based on a nine-square mandala representing the universe, with the royal palace at the center. Ancient Greek architectural orders like Doric, Ionic, and Corinthian influenced styles worldwide, and the golden ratio of 1.618 was incorporated into designs like the Parthenon and buildings as diverse as the Taj Mahal and United Nations headquarters.
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mathematics in architecture
The document discusses various architectural structures from around the world and through history that incorporate principles of geometry, mathematics, and the golden ratio. Many famous structures like the Parthenon, Taj Mahal, and Notre Dame used proportions and dimensions based on the golden ratio or other mathematical concepts. City planning in ancient India also incorporated mandalas and geometric patterns rooted in cosmological principles. Overall, the document shows how mathematics and principles of structure have long been applied in architectural design around the world.
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Mathematics applied in major fields of science and technology
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The document discusses the use of the golden ratio in architecture and its origins. It provides examples of how the golden ratio was used in ancient Egyptian architecture and the Great Pyramids. It also discusses Fibonacci's discovery of the Fibonacci sequence and how the golden ratio appears in this sequence as the terms grow large. Examples of the golden ratio in nature are also given. Le Corbusier's Modulor system for architectural proportions is described, which was based on the golden ratio. Analysis of the Parthenon and UN Secretariat building show they incorporate golden ratio proportions in their design.
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The Parthenon in Athens.pptx
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national parks of india
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tissue culture hybridization
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms for those who already suffer from conditions like anxiety and depression.
tissue culture hybridization
Tissue culture is a technique where small pieces of plant or animal tissue are cultured in a sterile medium outside of the organism. It was first developed in 1885 and has since been used extensively in medicine, agriculture, and research. It allows for the rapid duplication of plant materials while eliminating diseases and maintaining genetic traits. However, it requires specialized facilities and equipment and reduces genetic diversity.
tissue culture hybridization
Tissue culture is a technique where new plants are grown by removing plant tissue from the growing tip and placing it in an artificial medium where the cells divide rapidly to form a callus. The callus is then transferred to a medium containing hormones to promote growth and differentiation into plantlets. The plantlets are placed in soil to mature. Tissue culture allows many plants to be grown from one parent in disease-free conditions, and is commonly used for ornamental plants.
tissue culture hybridization
Plant tissue culture is a technique used in biotechnology where plant parts are grown in a sterile nutrient medium. It allows for micropropagation of plants through mitosis, saving time over traditional breeding. Explant material is sterilized and placed in a nutrient medium containing sugars, minerals, vitamins, and growth regulators. Cells dedifferentiate into callus which can then be grown into shoots or roots through manipulation of hormone levels in the medium. Plantlets are hardened before transplanting. Tissue culture was pioneered in the early 20th century and techniques have advanced, allowing mass production of plants for agriculture, research, and conservation of rare species.
tissue culture hybridization
The document discusses different types of hybrids that can occur between organisms, including intra-specific, interspecific, and intergeneric hybrids. It provides examples of both plant and animal hybrids that have been intentionally or naturally created, such as blood parrot cichlids, mule ducks, and killer bees. The document also covers concerns about hybridization between domesticated and wild species, as well as between purebred populations.
tissue culture hybridization
The document discusses different types of hybridization including single cross, double cross, three-way cross, and triple cross hybrids. It provides examples of hybrid animals like mules, ligers, and wholphins. Plant hybridization is more common than animal hybridization due to differences in pollination and chromosome doubling. The document notes that hybridization can threaten extinction if a population becomes entirely hybridized, and conservationists disagree on how to manage hybrid and pure populations.
tissue culture hybridization
Tissue culture is the propagation of plants using plant parts, single cells, or cell groups grown in a sterile, controlled environment. Banana is an important crop for India, contributing 37% of total fruit production. It grows best in tropical climates between 13-38°C with humidity of 75-85%. Good soil for banana has drainage, fertility, and moisture with a pH of 6-7.5. Common varieties include Grand Naine, which is becoming most popular for its stress tolerance and fruit quality. Land preparation involves adding organic matter to pits or furrows which are then planted with banana plants.
tissue culture hybridization
Tissue culture involves growing cells or tissues outside of the organism in a defined environment that can be easily manipulated. In 1885, Wilhelm Roux established the basic principle of tissue culture by maintaining a section of embryonic chicken tissue in saline solution. Modern tissue culture generally refers to growing cells from multicellular organisms in vitro. Tissue culture is an important tool for studying cell biology and provides a controlled environment for analysis. Plant tissue culture techniques allow for propagation of plants under sterile conditions and offer advantages over traditional propagation methods such as rapid cloning of desirable traits.
tissue culture hybridization
Modern plant tissue culture is performed under sterile conditions with filtered air. Plant materials from the environment are naturally contaminated with microorganisms, so they must be sterilized in chemical solutions like sodium hypochlorite or mercuric chloride. Explants are then placed on solid or liquid culture media composed of inorganic salts, organic nutrients, vitamins, and plant hormones to induce cell growth and differentiation. Solid media contain a gelling agent like purified agar.
tissue culture hybridization
Plant tissue culture, also known as micropropagation, uses sterilized plant parts or seeds placed in sterile containers with nutrient-rich gel medium to propagate plants. The explants are prevented from infection by microorganisms during rooting or multiplying. Exact copies of donor plants can be created using this method, which is useful for cloning plants with desirable traits faster than traditional propagation. The process involves establishing an aseptic culture, multiplying propagules, preparing propagules for soil transfer, and establishing plants in soil. Tissue culture allows for rapid multiplication of plants from a single explant in a brief period.
tissue culture hybridization
The document discusses techniques for something, though it does not provide many details on the specific techniques. It was written by an individual named jaisreenivasan. Overall the summary is limited due to the brevity of the original document which contains little contextual information.
tissue culture hybridization
Tissue culture is the growth of tissues or cells outside of the organism, typically using liquid, semi-solid, or solid growth media. In 1885, Wilhelm Roux established the basic principle of tissue culture by maintaining a section of embryonic chicken medullary plate in saline solution. In 1907, Ross Harrison demonstrated nerve cell growth in frog lymph. In 1913, Steinhardt et al. grew vaccinia virus in guinea pig corneal tissue fragments, establishing one of the earliest virus cultures.
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This document discusses different properties of 2D and 3D shapes including dimension, length, area, surface area, and volume. It defines each property and provides examples of when we experience these properties in everyday life such as measuring the length of an object, noticing the different sizes of pizza slices, wrapping presents, and measuring ingredients. The document contains visuals of common 3D shapes like spheres, cones, cubes, pyramids, and cylinders to help explain the concepts.
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Mathematics in architecture
- 7. Indians employed planning principles and proportions that rooted the buildings to the cosmos, considering the movements of sun, stars, and other heavenly bodies. vastu shastra , the ancient Indian canons of architecture and town planning employs mathematical drawings called mandalas
- 12. During the Indus Valley Civilization at the sites of Harappa and Mohenjo-Daro constructions took place following precise mathematical calculation
- 14. x x
- 26. Pythagoras theorem used in architecture: The Samrat Yantra, at Jaipur, designed by Jai Singh, measuring 147′ at its base and 90′ high could calculate time within two seconds accuracy per day. .
- 27. Jaipur was designed using the pithapada mandala as the basis. In this mandala of nine squares that represent the universe, earth occupies the central square. In the city, which consists of nine large squares, the central square is assigned to the royal palace. They calculated and planned city map using recursion: Length of City / Length of Middle Town : 771.1/340.5 ≈ 2.26; Length of Middle Town / Length of Castle: 340.5/151 ≈ 2.26
- 30. Great Mosque of Kairouan
- 32. The grand Imam Mosque
- 36. Here (a + b) / a = a/b= Φ ≈1.6180339887 Golden ratio is (a+b):a or a:b which is 1: Φ i.e. 1: 1.6180339887…
- 41. The Greek used it extensively for beauty and balance in the design of the Parthenon and other architecture:
- 42. Φ was used it in the design of Notre Dame in Paris, which was built in the 1163 and 1250
- 43. In India, Φ was used in the construction of the Taj Mahal,
- 44. Φ was used in the UN building
- 45. The CN Tower in Toronto has contains the golden ratio in its design. The ratio of observation deck at 342 meters to the total height of 553.33 is 0.618 or phi, the reciprocal of Phi!