1. The author invented a new formula for calculating the area of an isosceles triangle based on Pythagorean theorem.
2. The formula is: Area = b(4a^2 - b^2)/4, where b is the base and a is the length of the two equal sides.
3. The author provides two examples calculating the areas of isosceles triangles using the new formula and verifies the results using Heron's formula.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
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International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
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IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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zkStudyClub - Reef: Fast Succinct Non-Interactive Zero-Knowledge Regex ProofsAlex Pruden
This paper presents Reef, a system for generating publicly verifiable succinct non-interactive zero-knowledge proofs that a committed document matches or does not match a regular expression. We describe applications such as proving the strength of passwords, the provenance of email despite redactions, the validity of oblivious DNS queries, and the existence of mutations in DNA. Reef supports the Perl Compatible Regular Expression syntax, including wildcards, alternation, ranges, capture groups, Kleene star, negations, and lookarounds. Reef introduces a new type of automata, Skipping Alternating Finite Automata (SAFA), that skips irrelevant parts of a document when producing proofs without undermining soundness, and instantiates SAFA with a lookup argument. Our experimental evaluation confirms that Reef can generate proofs for documents with 32M characters; the proofs are small and cheap to verify (under a second).
Paper: https://eprint.iacr.org/2023/1886
Pushing the limits of ePRTC: 100ns holdover for 100 daysAdtran
At WSTS 2024, Alon Stern explored the topic of parametric holdover and explained how recent research findings can be implemented in real-world PNT networks to achieve 100 nanoseconds of accuracy for up to 100 days.
Le nuove frontiere dell'AI nell'RPA con UiPath Autopilot™UiPathCommunity
In questo evento online gratuito, organizzato dalla Community Italiana di UiPath, potrai esplorare le nuove funzionalità di Autopilot, il tool che integra l'Intelligenza Artificiale nei processi di sviluppo e utilizzo delle Automazioni.
📕 Vedremo insieme alcuni esempi dell'utilizzo di Autopilot in diversi tool della Suite UiPath:
Autopilot per Studio Web
Autopilot per Studio
Autopilot per Apps
Clipboard AI
GenAI applicata alla Document Understanding
👨🏫👨💻 Speakers:
Stefano Negro, UiPath MVPx3, RPA Tech Lead @ BSP Consultant
Flavio Martinelli, UiPath MVP 2023, Technical Account Manager @UiPath
Andrei Tasca, RPA Solutions Team Lead @NTT Data
Enhancing Performance with Globus and the Science DMZGlobus
ESnet has led the way in helping national facilities—and many other institutions in the research community—configure Science DMZs and troubleshoot network issues to maximize data transfer performance. In this talk we will present a summary of approaches and tips for getting the most out of your network infrastructure using Globus Connect Server.
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.
Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Removing Uninteresting Bytes in Software FuzzingAftab Hussain
Imagine a world where software fuzzing, the process of mutating bytes in test seeds to uncover hidden and erroneous program behaviors, becomes faster and more effective. A lot depends on the initial seeds, which can significantly dictate the trajectory of a fuzzing campaign, particularly in terms of how long it takes to uncover interesting behaviour in your code. We introduce DIAR, a technique designed to speedup fuzzing campaigns by pinpointing and eliminating those uninteresting bytes in the seeds. Picture this: instead of wasting valuable resources on meaningless mutations in large, bloated seeds, DIAR removes the unnecessary bytes, streamlining the entire process.
In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
Climate Impact of Software Testing at Nordic Testing DaysKari Kakkonen
My slides at Nordic Testing Days 6.6.2024
Climate impact / sustainability of software testing discussed on the talk. ICT and testing must carry their part of global responsibility to help with the climat warming. We can minimize the carbon footprint but we can also have a carbon handprint, a positive impact on the climate. Quality characteristics can be added with sustainability, and then measured continuously. Test environments can be used less, and in smaller scale and on demand. Test techniques can be used in optimizing or minimizing number of tests. Test automation can be used to speed up testing.
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.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
Welcome to the first live UiPath Community Day Dubai! Join us for this unique occasion to meet our local and global UiPath Community and leaders. You will get a full view of the MEA region's automation landscape and the AI Powered automation technology capabilities of UiPath. Also, hosted by our local partners Marc Ellis, you will enjoy a half-day packed with industry insights and automation peers networking.
📕 Curious on our agenda? Wait no more!
10:00 Welcome note - UiPath Community in Dubai
Lovely Sinha, UiPath Community Chapter Leader, UiPath MVPx3, Hyper-automation Consultant, First Abu Dhabi Bank
10:20 A UiPath cross-region MEA overview
Ashraf El Zarka, VP and Managing Director MEA, UiPath
10:35: Customer Success Journey
Deepthi Deepak, Head of Intelligent Automation CoE, First Abu Dhabi Bank
11:15 The UiPath approach to GenAI with our three principles: improve accuracy, supercharge productivity, and automate more
Boris Krumrey, Global VP, Automation Innovation, UiPath
12:15 To discover how Marc Ellis leverages tech-driven solutions in recruitment and managed services.
Brendan Lingam, Director of Sales and Business Development, Marc Ellis
A tale of scale & speed: How the US Navy is enabling software delivery from l...sonjaschweigert1
Rapid and secure feature delivery is a goal across every application team and every branch of the DoD. The Navy’s DevSecOps platform, Party Barge, has achieved:
- Reduction in onboarding time from 5 weeks to 1 day
- Improved developer experience and productivity through actionable findings and reduction of false positives
- Maintenance of superior security standards and inherent policy enforcement with Authorization to Operate (ATO)
Development teams can ship efficiently and ensure applications are cyber ready for Navy Authorizing Officials (AOs). In this webinar, Sigma Defense and Anchore will give attendees a look behind the scenes and demo secure pipeline automation and security artifacts that speed up application ATO and time to production.
We will cover:
- How to remove silos in DevSecOps
- How to build efficient development pipeline roles and component templates
- How to deliver security artifacts that matter for ATO’s (SBOMs, vulnerability reports, and policy evidence)
- How to streamline operations with automated policy checks on container images
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdfPaige Cruz
Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
F0261036040
1. International Journal of Engineering Science Invention
ISSN (Online): 2319 – 6734, ISSN (Print): 2319 – 6726
www.ijesi.org Volume 2 Issue 6ǁ June. 2013 ǁ PP.36-40
www.ijesi.org 36 | Page
Invention of the plane geometrical formulae - Part II
Mr. Satish M. Kaple
Asst. Teacher Mahatma Phule High School, Kherda, Jalgaon (Jamod) - 443402 Dist- Buldana,
Maharashtra (India)
ABSTRACT: In this paper, I have invented the formulae for finding the area of an Isosceles triangle. My
finding is based on Pythagoras theorem.
I. INTRODUCTION
A mathematician called Heron invented the formula for finding the area of a triangle, when all the three
sides are known. Similarly, when the base and the height are given, then we can find out the area of a triangle.
When one angle of a triangle is a right angle, then we can also find out the area of a right angled triangle. Hence
forth, We can find out the area of an equilateral triangle by using the formula of an equilateral triangle. These
some formulae for finding the areas of a triangles are not exist only but including in educational curriculum also.
But, In educational curriculum. I don’t appeared the formula for finding the area of an
isosceles triangle with doing teaching – learning process . Hence, I have invented the new formula for finding
the area of an isosceles triangle by using Pythagoras theorem.
I used pythagoras theorem with geometrical figures and algebric equations for the invention of the new
formula of the area of an isosceles triangle. I Proved it by using geometrical formulae & figures, 20 examples
and 20 verifications (proofs).
Here myself is giving you the summary of the research of the plane geometrical formulae- Part II
II. METHOD
First taking an isosceles triangle ABC A
B C
Fig. No. -1
Now taking a, a & b for the lengths of three sides of ABC
A
B C
Fig. No. – 2
2. Invention Of The Plane Geometrical Formulae - Part II
www.ijesi.org 37 | Page
Draw perpendicular AD on BC.
A
a a
B b/2 D b/2 C
b
Fig. No. - 3
ABC is an isosceles triangle and it is an acute angle also.
In ABC,
Let us represent the lengths of the sides of a triangle with the letters a,a,b. Side AB and side AC are congruent
side. Third side BC is the base. AD is perpendicular to BC.
Hence, BC is the base and AD is the height.
Here, taking AB=AC = a
Base , BC = b Height, AD = h
In ABC, two congruent right angled triangle are also formed by the length of perpendicular AD drawn on the
side BC from the vertex A. By the length of perpendicular AD drawn on the side BC, Side BC is divided into
two equal parts of segment. Therefore, these two equal segments are seg DB and seg DC. Similarly, two a right
angled triangles are also formed, namely, ADB and ADC which are congruent.
Thus,
DB = DC = 1/2 × BC
DB = DC = 1/2 × b = b/2
ADB and ADC are two congruent right angled triangle.
Taking first right angled ADC,
In ADC, Seg AD and Seg DC are both sides forming
the right angle. Seg AC is the hypotenuse.
A
Here, AC =a
Height , AD = h h a
DC = b/2 and m ADC = 900
D b/2 C
Fig. No - 4
According to Pythagoras Theorem,
(hypotenuse) 2
= ( one side forming the right angle) 2
+ ( second side forming the right angle) 2
In short,
( Hypotenuse ) 2
= ( one side) 2
+ ( second side) 2
AC2
= AD2
+ DC2
AD2
+ DC2
= AC2
h2
+ ( b/2 ) 2
= a2
h2
= a2
– (b/2) 2
h2
= a2
– b2
4
h2
= a2
× 4 – b2
4 4
h2
= 4a2
– b2
4 4
h2
= 4a2
– b2
4
Taking the square root on both side,
h2
= 4a2
– b2
4
h
3. Invention Of The Plane Geometrical Formulae - Part II
www.ijesi.org 38 | Page
h2
= 1 × (4 a2
– b2
)
4
h2
= 1 × 4a2
- b2
4
The square root of h2
is h and the square root of ¼ is ½
.·. h = ½ × 4a2
– b2
.·. Height, h = ½ 4a2
– b2
.·. AD =h = ½ 4a2
– b2
Thus,
Area of ABC = ½ × Base × Height
= ½ × BC × AD
=½ × b × h
But Height, h = ½ 4a2
– b2
.·. Area of ABC = ½ × b × ½ 4a2
– b 2
.·. Area of ABC = b × 1 4a2
– b2
2 2
= b × 1 × 4a2
– b2
2 × 2
= b 4a2
– b2
4
.·. Area of an isosceles ABC = b 4a2
– b2
4
For example- Now consider the following examples:-
Ex. (1) If the sides of an isosceles triangle are 10 cm, 10 cm and 16 cm.
Find it’s area D
DEF is an isosceles triangle.
In DEF given alongside, 10cm 10 cm
l ( DE) = 10 cm.
l l ( DF) = 10 cm. l ( EF) = 16 cm
E 16 cm F
Fig No- 5
Let,
a = 10 cm
Base, b = 16 cm.
By using The New Formula of an isosceles triangle,
.·. Area of an isosceles DEF = A (DEF)
= b 4a2
- b2
4
= 16 × 4(10)2
– (16)2
4
= 4 × 4 × 100 – 256
= 4 × 400 – 256
= 4 × 144
The square root of 144 is 12
= 4 × 12 = 48 sq.cm.
4. Invention Of The Plane Geometrical Formulae - Part II
www.ijesi.org 39 | Page
.·. Area of an isosceles DEF = 48 sq.cm.
Verification:-
Here,
l (DE) = a = 10 cm.
l ( EF) = b = 16 cm.
l ( DF) = c = 10 cm.
By using the formula of Heron’s
Perimeter of DEF = a + b + c
= 10 + 16 + 10 = 36 cm
Semiperimeter of DEF,
S = a + b + c
2
S = 36
2
S = 18 cm.
.·.Area of an isosceles DEF = s (s– a) (s– b) (s– c)
= 18 × (18 – 10) × (18 –16) × (18–10)
= 18 × 8 × 2 × 8
= (18 × 2) × (8 × 8)
= 36 × 64
= 36 × 64
The square root of 36 is 6 and the square root of 64 is 8
= 6 × 8 = 48 sq.cm
.·. Area of DEF = 48 sq.cm
Ex. (2) In GHI, l (GH) = 5 cm, l (HI) = 6 cm and l (GI) = 5 cm.
Find the area of GHI.
G
GHI
is an isosceles triangle.
In GHI given alongside, 5cm 5cm
l ( GH ) = 5 cm.
l ( HI ) = 6 cm.
l ( GI ) = 5 cm H 6cm I
Fig No- 6
Let,
a = 5 cm
Base, b = 6 cm.
By using The New Formula of area of an isosceles triangle,
.·. Area of an isosceles GHI = b 4a2
– b2
4
= 6 × 4 × (5)2
– (6)2
4
The simplest form of 6 is 3
4 2
= 3 × ( 4 × 25) – 36
2
= 3 × 100 – 36
2
= 3 × 64
2
The square root of 64 is 8
5. Invention Of The Plane Geometrical Formulae - Part II
www.ijesi.org 40 | Page
= 3 × 8 = 3 × 8 = 24
2 2 2
= 12 sq.cm.
.·. Area of an isosceles GHI = 12 sq.cm.
Verification :-
Here,
l (GH) = a = 5 cm.
l (HI) = b = 6 cm.
l (GI) = c = 5 cm.
By using the formula of Heron’s
Perimeter of GHI = a + b + c
= 5 + 6 + 5
= 16 cm
Semiperimeter of GHI,
S = a + b + c
2
S = 16
2
S = 8 cm.
.·.Area of an isosceles GHI = s (s– a) (s– b) (s– c)
= 8 × (8 – 5) × (8 –6) × (8–5)
= 8 × 3 × 2 × 3
= (8 × 2) × (3 × 3)
= 16 × 9
= 144
The square root of 144 is 12
= 12 sq.cm
.·. Area of an isosceles GHI = 12 sq.cm.
Explanation:-
We observe the above solved examples and their verifications, it is seen that the values of solved examples by
using the new formula of an isosceles triangle and the values of their verifications are equal.
Hence, The new formula of the area of an isosceles triangle is proved.
CONCLUSIONS:-
Area of an isosceles triangle = b × 4a2
– b2
4
From the above new formula , we can find out the area of an isosceles triangle. This new formula is useful in
educational curriculum, building and bridge construction and department of land records. This new formula is
also useful to find the area of an isosceles triangular plots of lands, fields, farms, forests, etc. by drawing their
maps.
REFERENCES:-
1 Geometry concepts and Pythagoras theorem.