Nature of Mathematics and Pedagogical practicesLaxman Luitel
I presented this paper in mathematics education and society conference 2019 (Jan 28 - Feb 2) at University of Hyderabad, Hyderabad, India. Paper is available in the website of conference and the link given below.
https://www.researchgate.net/publication/331113612
What patterns can we find in nature? Plants, flowers and fruits have all kinds of patterns, from petal numbers that are in the Fibonacci sequence, to symmetry, fractals and tessellation.
Nature of Mathematics and Pedagogical practicesLaxman Luitel
I presented this paper in mathematics education and society conference 2019 (Jan 28 - Feb 2) at University of Hyderabad, Hyderabad, India. Paper is available in the website of conference and the link given below.
https://www.researchgate.net/publication/331113612
What patterns can we find in nature? Plants, flowers and fruits have all kinds of patterns, from petal numbers that are in the Fibonacci sequence, to symmetry, fractals and tessellation.
This was an Inter Collegiate and a State Level Contest named SIGMA '08. Won a special prize for this paper. This research emphasized on how simple concepts of Mathematics helps into constructing complex mathematical models for space programming and their individual importance in real time applications.
CuriOdyssey is exploring nine visual patterns found in nature in a series of blog posts and in our upcoming new exhibit, THE NATURE OF PATTERNS. The patterns we will delve into are:
1. Symmetries (mirror & radial)
2. Fractals (branching)
3. Spirals
4. Flow and chaos
5. Waves and dunes
6. Bubbles and foam
7. Arrays and tiling (tessellations)
8. Cracks
9. Spots & stripes
These beautiful patterns are seen throughout the natural world, from atomic to the astronomical scale.
Philip Ball's book, "Patterns in Nature" was a source of inspiration. We recommend it to discover more about nature's incredible patterns.
This was an Inter Collegiate and a State Level Contest named SIGMA '08. Won a special prize for this paper. This research emphasized on how simple concepts of Mathematics helps into constructing complex mathematical models for space programming and their individual importance in real time applications.
CuriOdyssey is exploring nine visual patterns found in nature in a series of blog posts and in our upcoming new exhibit, THE NATURE OF PATTERNS. The patterns we will delve into are:
1. Symmetries (mirror & radial)
2. Fractals (branching)
3. Spirals
4. Flow and chaos
5. Waves and dunes
6. Bubbles and foam
7. Arrays and tiling (tessellations)
8. Cracks
9. Spots & stripes
These beautiful patterns are seen throughout the natural world, from atomic to the astronomical scale.
Philip Ball's book, "Patterns in Nature" was a source of inspiration. We recommend it to discover more about nature's incredible patterns.
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")[1] in everyday language refers to a sense of harmonious and beautiful proportion and balance.[2][3][a] In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, theoretic models, language, music and even knowledge itself.[4][b]
This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry.
In geometry[edit]
Main article: Symmetry (geometry)
The triskelion has 3-fold rotational symmetry.
A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion.[5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. The type of symmetry is determined by the way the pieces are organized, or by the type of transformation:
An object has reflectional symmetry (line or mirror symmetry) if there is a line going through it which divides it into two pieces which are mirror images of each other.[6]
An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.[7]
An object has translational symmetry if it can be translated without changing its overall shape.[8]
An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.[9]
An object has scale symmetry if it does not change shape when it is expanded or contracted.[10] Fractals also exhibit a form of scale symmetry, where small portions of the fractal are similar in shape to large portions.[11]
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
8. PROCEDURE 1:
Take a tour (at least 20
minutes) outside
the room and look around the
surroundings.
9. PROCEDURE 2:
As you walk around, take a
close-up picture of things that
naturally exists in the place
example: a leaf, a flower, an
insect such as butterfly, a bird,
etc.
10. PROCEDURE 3:
After the tour, print the
pictures. Make sure that
each picture is large enough
to studied.
11. PROCEDURE 4:
Observe the pictures. Is there any
possible way in which you can fold the
picture such that the parts of the objects
in the picture will become identical to
each other?
12. PROCEDURE 5:
Once you identified a way,
Use the editor of your
gallery to mark the line of
symmetry.
13. PROCEDURE 6:
Sort the pictures into two
groups – one for those objects
where there is symmetry and
one for those which don’t have.
14. PROCEDURE 7:
Explain in your paper
the pictures you
captured, why is it a
symmetry and the one
not.
23. Patterns maybe regular, repeated
or recurring forms of design. And
these patterns are occurring in
your day-today lives.
24. Patterns are commonly observed in
natural objects such as the six-fold
symmetry of snowflakes, the
hexagonal structure and
formation of honeycombs, the tiger's
stripes and hyena's spots, the
number of seeds in a sunflower, the
spiral of the snail's shell, and the
number of petals of flowers and
many more
25. It is said that humans are
hardwired to
recognize patterns, and by
studying patterns,
we discovered the underlying
mathematical principles
behind nature's design
26. In the general sense of the
word, patterns are regular,
repeated, or recurring forms
of design. We see patterns
every day.
30. an object is said to have symmetry
when it remains unchanged after
transformations such as
rotations and scaling are applied into
it.
SYMMETRY
31.
32. FRACTALS
are never ending patterns that are
self-similar across different scales.
These implies that zooming in the
lens on the digital image of the object
(fractal) do not give new details.
40. What is its significance
to your
day-to-day life?
41. Pattern indicates a sense
of structure and organization that it
seems only humans are capable
of producing these intricate, creative
and amazing formations.
It is in this perspective that some
people see an intelligent design
in the way that nature forms.
42.
43. Probably, you still recall that symmetry
indicates that you can draw an
imaginary line across
an object and the resulting
parts are mirror images of each other.
44.
45. This type of symmetry is known
as line or bilateral symmetry. It
is evident in most animals
including humans. The face of a
human follows this type of
symmetry. If you look on a mirror,
you will notice that the left and
right sides of your
face closely match.
47. 1.REFLECTION SYMMETRY
also called mirror symmetry
or line symmetry. It is made with
a line going through an object
which divides it into two pieces
which are mirror images of each
other.
48.
49. ROTATIONAL SYMMETRY
also called radial symmetry.
In Biology, this kind of symmetry
is exhibited by objects when their
similar parts are regularly arranged
around a central axis and the pattern
looks the same after a certain
amount of rotation.
56. FRACTALS
are the 'never-ending' patterns
that repeat indefinitely as the pattern
is iterated on an infinitely smaller
scale. We see this type of pattern in
trees, rivers, mountains, shells,
clouds, leaves, lightning, and more.
57.
58. SPIRALS
are another common pattern in nature that
we see more often in living things. Think
of the horns of a sheep, the shell of a
nautilus, and the placement of leaves
around a stem. A special type of spiral,
the logarithmic spiral,is one that gets
smaller as it goes.We see this pattern
in hurricanes, galaxies, and some seashells.
