This the power point presentation I made and used for my presentation in History of Math. Pardon me for not being able to cite ALL of my references through out the presentation. (one day I will). It is not detailed and perfect, but I am hoping that in a way, it may help you a hint on where to start to study about him and his works.
Information known about his life and SOME of his contributions will be found in this books. I merely focused on his first book, liber abbaci, so if you wish to see more of his contributions, look out for his other writings. (there are lots of articles online about him, just look for them and read them)
Fibonacci, the most famous mathematician from Pisa, Italy during the medieval period, is the man behind the fibonacci sequence and the popularization of the Hindu-Arabic Numeral System to Europe. Learn some things about him and his contributions through this.
Thank you :)
History of Math is a project in which students worked together in learning about historical development of mathematical ideas and theories. They were exploring about mathematical development from Sumer and Babylon till Modern age, and from Ancient Greek mathematicians till mathematicians of Modern age, and they wrote documents about their explorations. Also they had some activities in which they could work "together" (like writing a dictionary, taking part in the Eratosthenes experiment, measuring and calculating the height of each other schools, cooperating in given tasks) and activities that brought out their creativity and Math knowledge (making Christmas cards with mathematical details and motives and celebrating the PI day). Also they were able to visit Museum, exhibition "Volim matematiku" and to prepare (and lead) workshops for the Evening of mathematics (Večer matematike). At the end they have presented their work to other students and teachers.
This the power point presentation I made and used for my presentation in History of Math. Pardon me for not being able to cite ALL of my references through out the presentation. (one day I will). It is not detailed and perfect, but I am hoping that in a way, it may help you a hint on where to start to study about him and his works.
Information known about his life and SOME of his contributions will be found in this books. I merely focused on his first book, liber abbaci, so if you wish to see more of his contributions, look out for his other writings. (there are lots of articles online about him, just look for them and read them)
Fibonacci, the most famous mathematician from Pisa, Italy during the medieval period, is the man behind the fibonacci sequence and the popularization of the Hindu-Arabic Numeral System to Europe. Learn some things about him and his contributions through this.
Thank you :)
History of Math is a project in which students worked together in learning about historical development of mathematical ideas and theories. They were exploring about mathematical development from Sumer and Babylon till Modern age, and from Ancient Greek mathematicians till mathematicians of Modern age, and they wrote documents about their explorations. Also they had some activities in which they could work "together" (like writing a dictionary, taking part in the Eratosthenes experiment, measuring and calculating the height of each other schools, cooperating in given tasks) and activities that brought out their creativity and Math knowledge (making Christmas cards with mathematical details and motives and celebrating the PI day). Also they were able to visit Museum, exhibition "Volim matematiku" and to prepare (and lead) workshops for the Evening of mathematics (Večer matematike). At the end they have presented their work to other students and teachers.
Talk given by Professor Brian Schwartz at the Bloomberg School of Public Health about the environmental changes occurring because of oil consumption, pollution and population growth. Worth the gander. The problems presented here can only be solved by collective action of all of us, a different policy direction and by reassessing our fundamental values. Without all of these things happening, life as we know it will likely come to an end in our lifetime!
In this original Digital Art and Philosophy class, we will become familiar with different forms of digital art and related philosophical issues. Digital art is anything related to computers and art such as using a computer to create art or an art display that is digitized. Philosophical aspects arise regarding art, identity, performance, interactivity, and the process of creation. Students may respond to the material in essay, performance, or digital art work (optional). Instructor: Melanie Swan. Syllabus: www.MelanieSwan.com/PCA
Raising the benefits of meteorological services and satellitesEUMETSAT
In this presentation, given at the WMO side event during the 2014 EUMETSAT Meteorological Satellite Conference in Geneva, Stephan Bojinski (Satellite Utilization and Products Division, Space Programme, WMO) demonstrates how the WMO assists in raising the benefits from meteorological services and satellites and discusses the challenges faced in the future.
This ppt slide is all about number system. here we learn-
To represent numbers
To know about different system
How number system works
The study of numbers is not only related to computers. We apply numbers everyday, and knowing how numbers work, will give us an insight of how computers manipulate and store numbers.
The Mesopotamian culture is often called Babylonian, after the lar.docxoreo10
The Mesopotamian culture is often called Babylonian, after the large metropolis of that name. We could “babble on”1 and on about their many fine achievements in architecture, irrigation, and commerce, but it is their mathematics that is truly remarkable, dwarfing that of other contemporary civilizations. One might not be impressed by their use of a vertical mark for “one” and a horizontal mark for “ten” – ten being a common unit in the mathematics of many societies, including Egypt, China, Rome, and our own society today. On the other hand, they were the first to employ a “positional” system which, except for minor changes, survives to this day!
1The authors would like to apologize for the easy pun, but we couldn’t resist.
Let’s remind ourselves how our current number system works. It does not suffice to say that it is based on grouping by tens. The Egyptians did this – yet we have left them in the dust by taking a giant step forward to the “position system.” We require only ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Nevertheless, we can handle numbers of any size without the need to define a new symbol. This is because the value of a number is determined not just by the symbol. We must note the positionof the symbol as well. The two 3’s in the number 373 represent different quantities. You would rather have three hundred dollars than three dollars, right? To summarize, our number system employs a mere ten symbols, whose values depend on their position in the number. Moving one digit to the left multiplies its place value by ten, while moving to the right (not surprisingly) divides its place value by ten.
Observe, by the way, that this is true on both sides of the decimal point! In the number 3.1416, the 1 near the 6 is worth only one hundredth of the 1 near the 3. There is no number in the entire universe that is too large or too small for our clever (ten-digit!) number system (of Hindu-Arabic origin, by the way). We call our system the decimal system, because ten is the base.
The Babylonians used instead the sexagesimal system because they chose 60 as their base. While we are not sure why, we are fairly certain they did not have 60 fingers. One theory (which is very popular) is that 60 has a multitude of factors, that is, many numbers go into 60. Put another way, $60 can be divided without coin among 2, 3, 4, 5, 6, 10, 12, 15, 20, or 30 people. We shall follow the common practice of using commas to separate groups. Thus (3, 50)60 shall mean 3 sixties and 50 ones for a total of 230. What does (2, 3, 50)60 mean? Well in our position system, 357 means 3 hundreds, 5 tens, and 7 ones, right? Each column is ten times more valuable than its neighbor. In the same way, each column to the left in the Babylonian system is sixty times bigger! In the number (2, 3, 50)60, the 2 represents 2 3600’s – because 60 × 60 = 3600. The next column to the left would represent 60 × 3600 or 216000.
The Babylonians only used two symbols: a vertical mark for 1 and ...
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
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The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
SAP Sapphire 2024 - ASUG301 building better apps with SAP Fiori.pdfPeter Spielvogel
Building better applications for business users with SAP Fiori.
• What is SAP Fiori and why it matters to you
• How a better user experience drives measurable business benefits
• How to get started with SAP Fiori today
• How SAP Fiori elements accelerates application development
• How SAP Build Code includes SAP Fiori tools and other generative artificial intelligence capabilities
• How SAP Fiori paves the way for using AI in SAP apps
Welocme to ViralQR, your best QR code generator.ViralQR
Welcome to ViralQR, your best QR code generator available on the market!
At ViralQR, we design static and dynamic QR codes. Our mission is to make business operations easier and customer engagement more powerful through the use of QR technology. Be it a small-scale business or a huge enterprise, our easy-to-use platform provides multiple choices that can be tailored according to your company's branding and marketing strategies.
Our Vision
We are here to make the process of creating QR codes easy and smooth, thus enhancing customer interaction and making business more fluid. We very strongly believe in the ability of QR codes to change the world for businesses in their interaction with customers and are set on making that technology accessible and usable far and wide.
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Ever since its inception, we have successfully served many clients by offering QR codes in their marketing, service delivery, and collection of feedback across various industries. Our platform has been recognized for its ease of use and amazing features, which helped a business to make QR codes.
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At ViralQR, here is a comprehensive suite of services that caters to your very needs:
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Additionally, there is a 14-day free offer to ViralQR, which is an exceptional opportunity for new users to take a feel of this platform. One can easily subscribe from there and experience the full dynamic of using QR codes. The subscription plans are not only meant for business; they are priced very flexibly so that literally every business could afford to benefit from our service.
Why choose us?
ViralQR will provide services for marketing, advertising, catering, retail, and the like. The QR codes can be posted on fliers, packaging, merchandise, and banners, as well as to substitute for cash and cards in a restaurant or coffee shop. With QR codes integrated into your business, improve customer engagement and streamline operations.
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Subscribers of ViralQR receive detailed analytics and tracking tools in light of having a view of the core values of QR code performance. Our analytics dashboard shows aggregate views and unique views, as well as detailed information about each impression, including time, device, browser, and estimated location by city and country.
So, thank you for choosing ViralQR; we have an offer of nothing but the best in terms of QR code services to meet business diversity!
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
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In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
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See how to accelerate model training and optimize model performance with active learning
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5. Timeline of Ancient Egyptian Civilization Prehistoric Era Lower Paleolithic Age 200000 – 90000 B.C. Middle Paleolithic Age 90000 – 30000 B.C. Late Paleolithic Age 30000 - 7000 B.C. Neolithic Age 7000 - 4800 B.C.
6. Egypt Egyptian civilization begins more than 6000 years ago, with the largest pyramids built around 2600 B.C.
7. Timeline of Ancient Egyptian Civilization Predynastic Period Upper Egypt Badarian Culture 4800 – 4200 B.C. Amratian Culture (Al Amrah) 4200 – 3700 B.C. Gersean Cultures A & B (Al Girza) 3700 – 3150 B.C. * 365 day Calendar by 4200 B.C. * From 3100 B.C exhibited numbers in millions Lower Egypt Fayum A Culture (Hawara) 4800 – 4250 B.C. Merimda Culture 4500 – 3500 B.C. (Merimda Bani Salamah)
8.
9. Timeline of Ancient Egyptian Civilization Dynastic Period Early dynastic period 3150 – 2685 B.C. (Dynasties 1 & 2) Old Kingdom 2685 – 2160 B.C. (Dynasties 3 to 8) In about 2600 B.C, the Great Pyramid at Giza is constructed First Intermediate Period 2160 – 2040 B.C. (Dynasties 9 to 11) Middle Kingdom 1991 – 1668 B.C. (Dynasties 12 & 13) 1850 BC “Moscow Papyrus” contains 25 mathematical problems
11. Timeline of Ancient Egyptian Civilization Dynastic Period Second Intermediate Period 1668 - 1570 B.C. (Dynasties 14 to 17) 1650 BC “Ahmes Papyrus’ contains 85 mathematical problems New Kingdom 1570 - 1070 B.C. (Dynasties 18 to 20) Late Period 1070 - 712 B.C. (Dynasties 21 to 24) Dynasty 25 (Kushite domination) 712 – 671 B.C. Assyrian Domination Saite Period (Dynasty 26) 671 - 525 B.C. Dynasties 27 to 31 525 – 332 B.C Persian Period
12. Ahmes Papyrus (Rhind) Part of the Rhind papyrus written in hieratic script about 1650 B.C. It is currently in the British Museum. It started with a premise of “ a thorough study of all things, insight into all that exists, knowledge of all obscure secrets. ” It turns out that the script contains method of multiply and divide, including handling of fractions, together with 85 problems and their solutions .
14. Rosetta Stone & Egyptian Language The stone of Rosette is a basalt slab (114x72x28cm) that was found in 1799 in the Egyptian village of Rosette (Rashid). Today the stone is kept at the British Museum in London. It contains three inscriptions that represent a single text in three different variants of script, a decree of the priests of Memphis in honor of Ptolemalos V (196 BC). The text appears in form of hieroglyphs (script of the official and religious texts), of Demotic (everyday Egyptian script), and in Greek. The representation of a single text of the three script variants enabled the French scholar Jean Francois Champollion in 1822 to basically to decipher the hieroglyphs. Furthermore, with the aid of the Coptic language, he succeeded to realize the phonetic value of the hieroglyphs. This proved the fact that hieroglyphs do not have only symbolic meaning, but that they also served as a “spoken language”.
15. Egyptian Hieroglyphs This is the hieroglyphic inscription above the Great pyramid’s entrance. Egyptian written language evolved in three stages: Hieroglyphs Hieratic Coptic (spoken only)
16. Egyptian Numbers The knob of King Narmer, 3000BC The numerals occupy the center of the lower register. Four tadpoles below the ox, each meaning 100,000 record 400,000 oxen. The sky-lifting-god behind the goat was the hieroglyph for “one million”; together with the four tadpoles and the two “10,000” fingers below the goat, and the double “1,000” lotus-stalk below the god, this makes 1,422,000 goats. To the right of these animal quantities, one tadpole and two fingers below the captive with his arms tied behind his back count 120,000 prisoners. These quantities makes Narmer’s mace the earliest surviving document with numbers from Egypt, and the earliest surviving document with such large numbers from anywhere on the planet.
27. Egyptian Fractions 1/2 + 1/4 = 3/4 1/2 + 1/8 = 5/8 1/3 + 1/18 = 7/18 The Egyptians have no notations for general rational numbers like n / m , and insisted that fractions be written as a sum of non-repeating unit fractions (1/ m ). Instead of writing ¾ as ¼ three times, they will decompose it as sum of ½ and ¼.
28. Practical Use of Egyptian Fraction Divide 5 pies equally to 8 workers. Each get a half slice plus a 1/8 slice. 5/8 = 1/2 + 1/8
43. Egyptian Triangle Surveyors in ancient Egypt has a simple tool for making near-perfect right triangle: a loop rope divided by knots into twelve sections. When they stretched the rope to make a triangle whose sides were in the ratio 3:4:5, they knew that the largest angle was a right angle. The upright may be linked to the male, the base to the female and the hypotheses to the child of both. So Ausar (Osiris) may be regarded as the origin, Auset (Isis) as the recipient, and Heru (Horus) as perfected result.
44. Area of Rectangle The scribes found the areas of rectangles by multiplying length and breadth as we do today. Problem : 49 of RMP The area of a rectangle of length 10 khet (1000 cubits) and breadth 1 khet (100 cubits) is to be found 1000x100= 100,000 square cubits. The area was given by the scribe as 1000 cubits strips, which are rectangles of land, 1 khet by 1 cubit.
45.
46.
47. Area of triangle For the area of a triangle, ancient Egyptian used the equivalent of the formula A = 1/2bh. Problem : 51 of RMP The scribe shows how to find the area of a triangle of land of side 10 khet and of base 4 khet. The scribe took the half of 4, then multiplied 10 by 2 obtaining the area as 20 setats of land. Problem : 4 of MMP The same problem was stated as finding the area of a triangle of height (meret) 10 and base (teper) 4. No units such as khets or setats were mentioned.
48. Area of Circle Computing π Archimedes of Syracuse (250BC) was known as the first person to calculate π to some accuracy; however, the Egyptians already knew Archimedes value of π = 256/81 = 3 + 1/9 + 1/27 + 1/81 Problem : 50 of RMP A circular field has diameter 9 khet. What is its area? The written solution says, subtract 1/9 of the diameter which leaves 8 khet. The area is 8 multiplied by 8 or 64 khet. This will lead us to the value of π = 256/81 = 3 + 1/9 + 1/27 + 1/81 = 3.1605 But the suggestion that the Egyptian used is π = 3 = 1/13 + 1/17 + 1/160 = 3.1415
49.
50.
Editor's Notes
Homo [houmou] : man, sapien [s æpiən] : wise. Homo sapiens sapiens stands for wise, wise man.
1 million = 1,000,000; 1 billion = 1000 million.
1 million = 1,000,000; 1 billion = 1000 million.
The great pyramid is located near Giza. It was built by the Egyptian pharaoh Khufu around 2560 BC over a period of 20 years. When it was built, the Great pyramid was 146m. Over the years, it lost for 10 m off the top. It is the tallest structure on Earth for 4300 years. The base line is 229 m in length. It is a square to within 0.1% accuracy.
1 million = 1,000,000; 1 billion = 1000 million.
The great pyramid is located near Giza. It was built by the Egyptian pharaoh Khufu around 2560 BC over a period of 20 years. When it was built, the Great pyramid was 146m. Over the years, it lost for 10 m off the top. It is the tallest structure on Earth for 4300 years. The base line is 229 m in length. It is a square to within 0.1% accuracy.
1 million = 1,000,000; 1 billion = 1000 million.
Papyrus [p ə ’paiərəs]: paper made from the papyrus plant by cutting it in strips and pressing it flat; used by ancient Egyptians and Greeks and Romans. Tall sedge of the Nile valley yielding fiber that served many purposes in historic times. Rhind Papyrus perhaps is the oldest math text ever existed.
decipherThe name Rosetta refers to the crucial breakthrough in the research regarding Egyptian hieroglyphs. It especially represents the "translation" of "silent" symbols into a living language, which is necessary in order to make the whole content of information of these symbols accessible. The name Rosetta is attached to the stone of Rosette. This is a compact basalt slab (114x72x28 cm) that was found in July 1799 in the small Egyptian village Rosette (Raschid), which is located in the western delta of the Nile. Today the stone is kept at the British Museum in London. It contains three inscriptions that represent a single text in three different variants of script, a decree of the priests of Memphis in honour of Ptolemaios V. (196 b.c.). The text appears in form of hieroglyphs (script of the official and religious texts), of Demotic (everyday Egyptian script), and in Greek. The representation of a single text of the three mentioned script variants enabled the French scholar Jean Francois Champollion (1790-1832) in 1822 to basically decipher the hieroglyphs. Furthermore, with the aid of the Coptic language (language of the Christian descendants of the ancient Egyptians), he succeeded to realize the phonetic value of the hieroglyphs. This proved the fact that hieroglyphs do not have only symbolic meaning, but that they also served as a "spoken language".
This is the hieroglyphic inscription above the Great Pyramid ’s entrance. From http://www.catchpenny.org/gpglyph.html Egyptian written language evolved in three stages, hieroglyphs, hieratic, and coptic (spoken only?).
The mace head recorded victory of the first King of Egypt. The numerals occupy the center of the lower register. Four tadpoles below the ox, each meaning 100,000, record 400,000 oxen. The sky- lifting Heh- god behind the goat was the hieroglyph for "one million"; together with the four tadpoles and the two "10,000" fingers below the goat, and the double "1,000" lotus- stalk below the god, this makes 1,422,000 goats. To the right of these animal quantities, one tadpole and two fingers below the captive with his arms tied behind his back count 120,000 prisoners. These quantities makes Narmer's mace the earliest surviving document with numbers from Egypt, and the earliest surviving document with such large numbers from anywhere on the planet.
Additive means that the order of these symbols does not matter.
To this day, it is not entirely clear how the Egyptians performed addition and subtractions.
A check means that this number will be counted to add up the desired multiplier or results. If we rotate 90 degree of the above figure, and use 1 for the check, and 0 for the non-check, we get a binary number represent of the number 13. “Eureka”, the Egyptians could have discovered binary numbers.
This is nothing but representing any positive integer as a binary expansion.
Power of 2 from k=0 to 8: 1, 2, 4, 8, 16, 32, 64, 128, 256.
Note that a + b = b + a is called commutative law, and a + ( b + c ) = ( a + b ) + c is called associative law.
Division and multiplication use the same method, except that the role of multiplier and result are interchanged. Need guess work, or not?
Of course, the result is 4 + 3/8, or 4.375. The Egyptians have not developed the concept of decimal fractions (0.375). They represent the result as 4 + ¼ + 1/8.
A web page on Egyptian fraction: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fractions/egyptian.html
Other formulas are also available, e.g., 2/(3k) = 1/(2k) + 1/(6k), or 2/n = 1/n + 1/(2n) + 1/(3n) + 1/(6n).
Picture from http://elfwood.lysator.liu.se/loth/j/u/juhaharju/mralothi.jpg.html Although they may count to two, they still have a very good sense of large or small. There are two aspects to numbers, cardinal (size, one, two, three, four, …) and ordinal (sequence, first, second, third, etc).
Picture from http://elfwood.lysator.liu.se/loth/j/u/juhaharju/mralothi.jpg.html Although they may count to two, they still have a very good sense of large or small. There are two aspects to numbers, cardinal (size, one, two, three, four, …) and ordinal (sequence, first, second, third, etc).
De-associate number from concrete objects is the first step in sharp the concept of numbers. See T. Dantzig, “Number, the Language of Science”, The Free Press, New York 1967, p.6.
De-associate number from concrete objects is the first step in sharp the concept of numbers. See T. Dantzig, “Number, the Language of Science”, The Free Press, New York 1967, p.6.
De-associate number from concrete objects is the first step in sharp the concept of numbers. See T. Dantzig, “Number, the Language of Science”, The Free Press, New York 1967, p.6.
De-associate number from concrete objects is the first step in sharp the concept of numbers. See T. Dantzig, “Number, the Language of Science”, The Free Press, New York 1967, p.6.
De-associate number from concrete objects is the first step in sharp the concept of numbers. See T. Dantzig, “Number, the Language of Science”, The Free Press, New York 1967, p.6.
De-associate number from concrete objects is the first step in sharp the concept of numbers. See T. Dantzig, “Number, the Language of Science”, The Free Press, New York 1967, p.6.
De-associate number from concrete objects is the first step in sharp the concept of numbers. See T. Dantzig, “Number, the Language of Science”, The Free Press, New York 1967, p.6.
De-associate number from concrete objects is the first step in sharp the concept of numbers. See T. Dantzig, “Number, the Language of Science”, The Free Press, New York 1967, p.6.
De-associate number from concrete objects is the first step in sharp the concept of numbers. See T. Dantzig, “Number, the Language of Science”, The Free Press, New York 1967, p.6.
This solid figure is also known as frustum. This problem was found in Moscow Papyrus. The Egyptians thought that the numbers and their mathematics are given by god; and they does not seem to have the need to justify their methods. Some of the formulas they devise may only be approximate. For example, in the Temple of Horus at Edfu delicatory inscription, area of the 4-sided quadrilateral was given the formula A = ( a + c )/( b + d )/4, where a , b , c , d are the lengths of the consecutive sides, which is incorrect.
This solid figure is also known as frustum. This problem was found in Moscow Papyrus. The Egyptians thought that the numbers and their mathematics are given by god; and they does not seem to have the need to justify their methods. Some of the formulas they devise may only be approximate. For example, in the Temple of Horus at Edfu delicatory inscription, area of the 4-sided quadrilateral was given the formula A = ( a + c )/( b + d )/4, where a , b , c , d are the lengths of the consecutive sides, which is incorrect.
This solid figure is also known as frustum. This problem was found in Moscow Papyrus. The Egyptians thought that the numbers and their mathematics are given by god; and they does not seem to have the need to justify their methods. Some of the formulas they devise may only be approximate. For example, in the Temple of Horus at Edfu delicatory inscription, area of the 4-sided quadrilateral was given the formula A = ( a + c )/( b + d )/4, where a , b , c , d are the lengths of the consecutive sides, which is incorrect.
This solid figure is also known as frustum. This problem was found in Moscow Papyrus. The Egyptians thought that the numbers and their mathematics are given by god; and they does not seem to have the need to justify their methods. Some of the formulas they devise may only be approximate. For example, in the Temple of Horus at Edfu delicatory inscription, area of the 4-sided quadrilateral was given the formula A = ( a + c )/( b + d )/4, where a , b , c , d are the lengths of the consecutive sides, which is incorrect.
This solid figure is also known as frustum. This problem was found in Moscow Papyrus. The Egyptians thought that the numbers and their mathematics are given by god; and they does not seem to have the need to justify their methods. Some of the formulas they devise may only be approximate. For example, in the Temple of Horus at Edfu delicatory inscription, area of the 4-sided quadrilateral was given the formula A = ( a + c )/( b + d )/4, where a , b , c , d are the lengths of the consecutive sides, which is incorrect.
This solid figure is also known as frustum. This problem was found in Moscow Papyrus. The Egyptians thought that the numbers and their mathematics are given by god; and they does not seem to have the need to justify their methods. Some of the formulas they devise may only be approximate. For example, in the Temple of Horus at Edfu delicatory inscription, area of the 4-sided quadrilateral was given the formula A = ( a + c )/( b + d )/4, where a , b , c , d are the lengths of the consecutive sides, which is incorrect.