-
Pages
Categories
Search this Blog
Archives
mAnasa-taraMgiNI supplement
- RT @ANI: #WATCH | Defence Minister Rajnath Singh performs 'Shastra Pooja' at Auli Military Station in Chamoli, Uttarakhand on the occasion… 16 hours ago
- https://t.co/miuxsAc3tT 16 hours ago
- Good work: deviantart.com/prehistorybyli… 18 hours ago
- Some aspects of geopolitics are simply too dangerous to state plainly in public. The discerning will get how the so… twitter.com/i/web/status/1… 18 hours ago
- Probably at some level this is the tip of the iceberg of the penetration by marUmatta & also pa~nchanetra-mlechCha-… twitter.com/i/web/status/1… 18 hours ago
Top Posts
-
Recent Posts
- A catalog of attractors, repellors, cycles, and other oscillations of some common functional iterates
- The wink of the Gorgon and the twang of the Lyre
- Some poems
- The Kaumāra cycle in the Skandapurāṇa’s Śaṃkara-saṃhitā
- Some notes on the runiform “Altaic” inscriptions and the early Turk Khaghanates: Orkhon and beyond
- Vikīrṇā viṣayāḥ: India and the Rus
- Alkaios’ hymn to the Dioskouroi: Hindu parallels
- Some notes on the Indo-European aspects of the Anatolian tradition
- The death of Miss Lizzie Willink
- Indo-European expansions and iconography: revisiting the anthropomorphic stelae
- Geopolitical summary: March 2022
- Human retroviruses, sociology of science, and biographical ruminations
- Transcripts of conversations: the addiction principle:
- Phantom impressions-1
- A note on Śrī, Viṣṇu and śṛṅgāra
- Are civilizational cycles the norm?
- On the rise of the mātṛkā-s and the goddess Cāmuṇḍā
- Huns, Uralics, and empires of the steppe
- Some observations on the Lekkerkerker-Zeckendorf decomposition of integers
- Subjective and objective insight
- On the passing of E.O. Wilson
- Some words on mleccha cartels
- Relationships between incircles of the “equilateral triangles in a square” system
- The Rāmāyaṇa in numbers: meters, sarga- and kāṇḍa- structure
- Sneha, snowstorms, the sun and the moon in enigmatic ṛk-s
- The strange case of the Āpastamba sprite
- Agni as the divine commander in the Veda and the Purāṇa
- The birth defects of Dhṛtarāṣṭra and Pāṇḍu and related matters
- The rise of Navyonmāda, the subversion of the Mahāmleccha-s, Cīnānusāra and beyond
- Some biographical reflections on visualizing irrationals
-
Join 693 other followers
Meta
-
October 2022 M T W T F S S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 -
Pages
Categories
Search this Blog
Archives
mAnasa-taraMgiNI supplement
- RT @ANI: #WATCH | Defence Minister Rajnath Singh performs 'Shastra Pooja' at Auli Military Station in Chamoli, Uttarakhand on the occasion… 16 hours ago
- https://t.co/miuxsAc3tT 16 hours ago
- Good work: deviantart.com/prehistorybyli… 18 hours ago
- Some aspects of geopolitics are simply too dangerous to state plainly in public. The discerning will get how the so… twitter.com/i/web/status/1… 18 hours ago
- Probably at some level this is the tip of the iceberg of the penetration by marUmatta & also pa~nchanetra-mlechCha-… twitter.com/i/web/status/1… 18 hours ago
Top Posts
-
Recent Posts
- A catalog of attractors, repellors, cycles, and other oscillations of some common functional iterates
- The wink of the Gorgon and the twang of the Lyre
- Some poems
- The Kaumāra cycle in the Skandapurāṇa’s Śaṃkara-saṃhitā
- Some notes on the runiform “Altaic” inscriptions and the early Turk Khaghanates: Orkhon and beyond
- Vikīrṇā viṣayāḥ: India and the Rus
- Alkaios’ hymn to the Dioskouroi: Hindu parallels
- Some notes on the Indo-European aspects of the Anatolian tradition
- The death of Miss Lizzie Willink
- Indo-European expansions and iconography: revisiting the anthropomorphic stelae
- Geopolitical summary: March 2022
- Human retroviruses, sociology of science, and biographical ruminations
- Transcripts of conversations: the addiction principle:
- Phantom impressions-1
- A note on Śrī, Viṣṇu and śṛṅgāra
- Are civilizational cycles the norm?
- On the rise of the mātṛkā-s and the goddess Cāmuṇḍā
- Huns, Uralics, and empires of the steppe
- Some observations on the Lekkerkerker-Zeckendorf decomposition of integers
- Subjective and objective insight
- On the passing of E.O. Wilson
- Some words on mleccha cartels
- Relationships between incircles of the “equilateral triangles in a square” system
- The Rāmāyaṇa in numbers: meters, sarga- and kāṇḍa- structure
- Sneha, snowstorms, the sun and the moon in enigmatic ṛk-s
- The strange case of the Āpastamba sprite
- Agni as the divine commander in the Veda and the Purāṇa
- The birth defects of Dhṛtarāṣṭra and Pāṇḍu and related matters
- The rise of Navyonmāda, the subversion of the Mahāmleccha-s, Cīnānusāra and beyond
- Some biographical reflections on visualizing irrationals
-
Join 693 other followers
Meta
-
October 2022 M T W T F S S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Tag Archives: triangles
Relationships between incircles of the “equilateral triangles in a square” system
This note relates to geometric relationships that may be likened to the Japanese temple-tablet problems. The inspiration for discovering and exploring it came from an origami construction presented by the pioneer in that field, Sundara Rao of Kumbhaghoṇa, in the … Continue reading
Johannes Germanus Regiomontanus and his rod
Even before we had become acquainted with the trigonometric sum and difference formulae or calculus are father had pointed to us that there was an optimal point at which one should stand to observe or photograph features on vertical structures, … Continue reading
A great statistician, and biographical, numerical musings on ancient game
Recently my friend brought it to my attention that C. Radhakrishna Rao had scored a century. Born in 1920 CE to Doraswamy Nayadu and A. Laxmikanthamma from the Andhra country, he is one of the great mathematical thinkers and statisticians … Continue reading
Rāsabha-nyāya-śikṣā
Vrishchika had been seeing several kids of patients affected by the chemical leak that had happened sometime ago. While she saw some purely for routine clinical practice, she was also particularly interested in the several cases exhibiting heterotaxy and had … Continue reading
The Mātrā-meru and convergence to a triangle
What is presented below will be elementary for someone with even just the mastery of secondary school mathematics. Nevertheless, even simple stuff might present points of interest to people who see beauty in such things. Consider the following question: Given … Continue reading
Posted in Scientific ramblings
Tagged fibonacci, geometry, Golden Ratio, mathematics, recreational geometry, sequence, triangles, trigonometry
Leave a comment
Some Nārāyaṇa-like convergents and their geometric and trigonometric connections
While playing with an iterative geometric construction in our youth we discovered for ourselves a particular right triangle whose sides are in the proportion , where is the Golden Ratio. This triangle is of course famous as being the basis … Continue reading
Some notes on rational sector triangle triples
Rational points on a unit circle There are some events that happen in the course of ones life that might be considered historical or world-changing. One such event from our lifetime is the proving of the Last Theorem of Fermat … Continue reading
The minimal triangle circumscribing a semicircle
Consider a fixed semicircle with center at and radius . Let be the isosceles triangle which circumscribes it (Figure 1). Figure 1 What will be the characteristics of the minimal form of the said triangle, i.e. triangle with minimum perimeter, … Continue reading
The Platonic culmination of Euclid and the pentagon-hexagon-decagon identity
Why did great sage Pāṇini compose the Aṣṭādhyāyī? There were probably multiple reasons but often you hear people say that he wanted to give a complete description of the Sanskrit language. That was probably one of his reasons but was … Continue reading
Posted in Heathen thought, Life
Tagged Geometric construction, geometry, Golden Ratio, Greek, Hindu, Plato, polygons, polyhedra, recreational geometry, religion, triangles, trigonometry
Leave a comment
Residues of squares, sequence curiosities and parabolas galore
Squares and their residues This is an exploration of number triangles in the same vein as some other such we have previously described . It resulted in some observations that seemed interesting to us. Some are perhaps trivial but some … Continue reading
Posted in Scientific ramblings
Tagged mathematical entity, mathematics, numbers, square root, squares, triangles
Leave a comment
Median and pedal triangles and derived fractals: an introductory account
It is rather easily seen that joining the midpoints of the sides of a triangle yields four congruent triangles that in turn are similar to the original triangle (Figure 1). This figure might be used to provided a self-evident geometric … Continue reading
Posted in art, Scientific ramblings
Tagged fractal, fractals, Geometric construction, geometry, mathematics, triangles
Leave a comment
Infinite bisections required for trisection of an angle
Figure 1: Self-evident demonstration of Figure 2: Application of the same as serial bisections to trisect the angle. In the example chosen here we have . In ten steps we get to which is a pretty close, though in principle … Continue reading
Posted in art, Scientific ramblings
Tagged Geometric construction, geometry, mathematics, recreational geometry, series sum, triangles, trisection
Leave a comment
Some meanderings among golden stuff-2
Related stuff: Golden Ratio-0 Golden Ratio-1 If the golden ratio can fascinate erudite men of high IQ then what to say of simpletons like us. Hence, we shall here talk about some more trivia in this regard. The golden ratio … Continue reading
Leaves from the scrapbook
There were extensive memoirs in the form of electronic scrapbooks of Somakhya, Lootika and some members of their circle. Those in the know read the available excerpts due to matters of considerable interest being recorded in them. Other parts were … Continue reading
Posted in art, Life
Tagged chaos, Geometric construction, geometry, ghost, ghosts, Lotka-Volterra, population dynamics, Story, triangles, trigonometry, trisection
Leave a comment
van Aubel’s theorem
The van Aubel’s theorem is a simple theorem which is comparable to the theorem attributed to the French conqueror Napoleon Bonaparte regarding triangles. It is easy to prove once you know the upāya, even as the yogin-s would say ānanda … Continue reading
Posted in art, Life, Scientific ramblings
Tagged Geometric construction, geometry, mathematics, philosophy, triangles, trigonometry, van Aubel
Leave a comment
Some trivia on equilateral triangles and the like
One may ask why one needs to revisit elementary geometry that was usually studied at secondary school. The simple answer is it is a good recreation. But it is not like any recreation, because it also opens the doors to … Continue reading
Posted in art, Life, Scientific ramblings
Tagged centroid, circumcenter, conics, Euler line, incenter, Kiepert hyperbola, Nagel line, Nagel point, Napoleon, nine-point circle, orthocenter, Spieker point, triangles
Leave a comment
mAnasa-taraMgiNI 