KENNESAW STATE UNIVERSITY ATHLETICS VISUAL IDENTITY

Size: px
Start display at page:

Download "KENNESAW STATE UNIVERSITY ATHLETICS VISUAL IDENTITY"

Transcription

1 KENNESAW STATE UNIVERSITY ATHLETICS VISUAL IDENTITY

2 KENNESAW STATE DEPARTMENT OF ATHLETICS VISUAL IDENTITY GENERAL University Athletics Brand History...3 Referencing the Institution...3 Referencing the Mascot...3 Color Palette...3 Usage Guidelines...3 Art Sheet...5 PRIMARY IDENTITY Logo Monogram... 7 SECONDARY IDENTITY Logo Owl Wordmark...8 WWWordmark...9 TERTIARY IDENTITY Owl...13 Owls Wordmark...13 Owl Head Talon TYPOGRAPHY Typeface Numerals...17 Supporting Typeface EQUIPMENT Uniform Options Olympic Sports Football...21 RESOURCES Appendix A...22 Appendix B...23 Appendix C Examples Of Misuse KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW

3 HISTORY Since its humble beginnings as an NAIA program in 1982, the Kennesaw State Department of Athletics has grown at a rate often unseen in college athletics. Originally known as the Golden Owls, the Department of Athletics went through a complete re-brand and debuted the current marks in June of This document is meant to serve as a comprehensive brand guide for users of the Kennesaw State Athletics visual identity. REFERENCING THE INSTITUTION The University should always be identified as Kennesaw State University or Kennesaw State. KSU or the Owls are acceptable for second and subsequent references. Kennesaw State should not be referred to as Kennesaw or K-State. REFERENCING THE MASCOT The mascot should always be identified as the Owls. The Kennesaw State Owls should not be referred to as Lady Owls or Fighting Owls. COLOR PALETTE PRIMARY SECONDARY TERTIARY KSU GOLD PANTONE 1235 C C0 M29 Y91 K0 R253 G187 B48 #FDBB30 BLACK PANTONE BLACK C C0 M0 Y0 K100 R11 G19 B21 #0B1315 GREY PANTONE 421 C C0 M0 Y0 K26 R197 G198 B200 #C5C6C8 USAGE GUIDELINES Monogram, Owl Wordmark, Wordmark, or Kennesaw State must be present on all apparel and outgoing communications. The logo may not be treated in any way, including patterns, except for cases approved by the Branding Committee. Logos may be used as design elements, if and only if, one of the primary logos is present. The primary marks should not be watermarked. KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW 3

4 KENNESAW STATE DEPARTMENT OF ATHLETICS VISUAL IDENTITY OVERVIEW PRIMARY ATHLETIC MARK SECONDARY ATHLETIC MARKS TERTIARY ATHLETIC MARKS FONTS KSU BOLD - STANDARD [FONT BOOK INCLUDES MEDIUM, MEDIUM ITALIC, BOLD, BOLD ITALIC] A B C D E F G H I J K L M N O P Q R S T U V W Y Z GOTHAM - SUPPORTING [FONT BOOK INCLUDES LIGHT, LIGHT ITALIC, BOOK, BOOK ITALIC, MEDIUM, MEDIUM ITALIC, BOLD, BOLD ITALIC] Aa Bb Cc Dd Ee Ff Gg Hh Ii Jj Kk Ll Mm Nn Oo Pp Qq Rr Ss Tt Uu Vv Ww x Yy Zz Aa Bb Cc Dd Ee Ff Gg Hh Ii Jj Kk Ll Mm Nn Oo Pp Qq Rr Ss Tt Uu Vv Ww x Yy Zz BANK GOTHIC - SUPPORTING [MUST BE USED IN ALL CAPS] A B C D E F G H I J K L M N O P Q R S T U V W Y Z PMS 1235 PANTONE PROCESS BLACK PMS 421 COLORS C 0 M 29 Y 91 K 0 C 100 M 100 Y 100 K 100 C 0 M 0 Y 0 K 26 R 253 G 187 B 48 R 253 G 187 B 48 R 253 G 187 B 48 ACCEPTABLE VERBIAGE WEB FDBB30 WEB 0B1315 WEB C5C6C8 Kennesaw State University, Kennesaw State, Kennesaw State Athletics or Kennesaw State Department of Athletics Second/Subsequent: KSU or The Owls Kennesaw State University Athletic Association Mascot: Owls NOT: Lady Owls or Fighting Owls

5 MONOGRAM The Monogram is the primary identity mark. Must be present on all apparel and outgoing communications if the Full Mark or Kennesaw State are not visible. Usage Guidelines: Patterned fill allowable only if approved by the branding committee. [See Appendix A] Interior of the KS must be lighter than the first stroke. = 1/5 HEIGHT OF KS PROTECTED AREA: The protected area around the logo ensures that no other graphic elements interfere with its clarity and integrity. The depth of the protected area is equivalent to the height of x. COLOR VARIATION The logo can be used in the following color variations: KS1 KS2 KS3 KS4 KS5 KS6 KS7 KS8 KS9 KS10 KS11 KS12 KS13 KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW 5

6 OWL WORDMARK The Owl Wordmark is a secondary identity mark. Must be present on all apparel and outgoing communications if the Monogram or Kennesaw State are not visible. Usage Guidelines: Wings must be darker than the face. Banner may indicate sport, but should not be gender specific. [See Appendix B for approved banners.] May not be printed/displayed smaller than 2.5in W proportionately. = 1/7 HEIGHT OF FULL LOGO PROTECTED AREA: The protected area around the logo ensures that no other graphic elements interfere with its clarity and integrity. The depth of the protected area is equivalent to the height of x. COLOR VARIATION The logo can be used in the following color variations: FM1 FM2 FM3 FM4 FM5 FM6 FM7 FM8 FM9 FM10 FM11 FM12 FM13 FM14 6 KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW

7 WORDMARK The Wordmark is a secondary identity mark. Usage Guidelines: Banner may indicate sport, but should not be gender specific. [See Appendix C for approved banners.] May not be printed/displayed smaller than 2.0in W proportionately. Kennesaw State must be lighter than the color of the stroke. = 1/8 HEIGHT OF WORDMARK PROTECTED AREA: The protected area around the logo ensures that no other graphic elements interfere with its clarity and integrity. The depth of the protected area is equivalent to the height of x. COLOR VARIATION The logo can be used in the following color variations: W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12 W13 KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW 7

8 KENNESAW STATE UNIVERSITY ATHLETICS TERTIARY IDENTITY Usage Guidelines: Should only be used in the presence of one of the primary or secondary marks. Only logos that may be watermarked. May not be printed/displayed at an opacity less than 15%. Must be smaller is size than the primary/secondary logo when printed/displayed at full opacity. 8 KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW

9 OWL The logo can be used in the following color variations: O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 O11 O12 O13 O14 OWL HEAD The logo can be used in the following color variations: OH1 OH2 OH3 OH4 OH5 OH6 OH7 OH9 OH10 OH10 OH11 OH12 OH13 OH14 KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW 9

10 TYPOGRAPHY Typeface KSU BOLD A B C D E F G H I J K L M N O P Q R S T U V W Y Z KSU BOLD ITALIC A B C D E F G H I J K L M N O P Q R S T U V W Y Z KSU MEDIUM A B C D E F G H I J K L M N O P Q R S T U V W Y Z KSU MEDIUM ITALIC A B C D E F G H I J K L M N O P Q R S T U V W Y Z 10 KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW

11 TYPOGRAPHY Numerals KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW 11

12 TYPOGRAPHY Supporting Typeface GOTHAM LIGHT A B C D E F G H I J K L M N O P Q R S T U V W Y Z a b c d e f g h i j k l m n o p q r s t u v w x y z GOTHAM LIGHT ITALIC A B C D E F G H I J K L M N O P Q R S T U V W Y Z a b c d e f g h i j k l m n o p q r s t u v w x y z GOTHAM BOOK A B C D E F G H I J K L M N O P Q R S T U V W Y Z a b c d e f g h i j k l m n o p q r s t u v w x y z GOTHAM BOOK ITALIC A B C D E F G H I J K L M N O P Q R S T U V W Y Z a b c d e f g h i j k l m n o p q r s t u v w x y z GOTHAM MEDIUM A B C D E F G H I J K L M N O P Q R S T U V W Y Z a b c d e f g h i j k l m n o p q r s t u v w x y z GOTHAM MEDIUM ITALIC A B C D E F G H I J K L M N O P Q R S T U V W Y Z a b c d e f g h i j k l m n o p q r s t u v w x y z GOTHAM BOLD A B C D E F G H I J K L M N O P Q R S T U V W Y Z a b c d e f g h i j k l m n o p q r s t u v w x y z GOTHAM BOLD ITALIC A B C D E F G H I J K L M N O P Q R S T U V W Y Z a b c d e f g h i j k l m n o p q r s t u v w x y z 12 KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW

13 TYPOGRAPHY Sport Specific Typeface BANK GOTHIC A B C D E F G H I J K L M N O P Q R S T U V W Y Z a b c d e f g h i j k l m n o p q r s t u v w x y z BANK GOTHIC CAPS TRACK & FIELD KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW 13

14 UNIFORM OPTIONS UNI1 UNI2 UNI3 UNI4 UNI5 UNI6 14 KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW

15 UNIFORM OPTIONS UNI7 UNI8 UNI9 UNI10 UNI11 UNI12 KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW 15

16 UNIFORM OPTIONS KENNESAW STATE UNI13 KENNESAW STATE UNI14 KENNESAW STATE UNI15 KENNESAW STATE UNI16 KENNESAW STATE UNI17 KENNESAW STATE UNI18 16 KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW

17 APPENDI A Approved on a case by case basis. Must be presented to and approved by the KSU Branding Committee before each use. OWL NETWORK OWL NETWORK OWL NETWORK OWL NETWORK KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW 17

18 APPENDI B Approved Banners - Full Mark 18 KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW

19 APPENDI C Approved Banners - Wordmark KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW 19

20 EAMPLES OF MISUSE NO GOLD PRINT ON GREY NO GOLD PRINT ON GREY NO GOLD PRINT ON GREY NO GOLD PRINT ON GREY NO WHITE STROKE NO WHITE STROKE NO WHITE STROKE NO WHITE STROKE NO WHITE STROKE NO WHITE STROKE NO WHITE STROKE NO WHITE STROKE NO WHITE STROKE NO WHITE STROKE NO WHITE STROKE NO WHITE STROKE NO WHITE STROKE INVERTED LOGO INVERTED LOGO INVERTED LOGO INVERTED LOGO INVERTED LOGO INVERTED LOGO INVERTED LOGO 20 KENNESAW STATE UNIVERSITY VISUAL IDENTITY OVERVIEW

ST. CLOUD TECHNICAL & COMMUNITY COLLEGE 1.02CYCLONES BRAND GUIDE TABLE OF CONTENTS

ST. CLOUD TECHNICAL & COMMUNITY COLLEGE 1.02CYCLONES BRAND GUIDE TABLE OF CONTENTS ST. CLOUD TECHNICAL & COMMUNITY COLLEGE 1.02CYCLONES BRAND GUIDE TABLE OF CONTENTS ST. CLOUD TECHNICAL & COMMUNITY COLLEGE CYCLONES BRAND GUIDELINES 1 INTRO 2 St. Cloud Technical & Community College thrives

More information

Terms of Use. Copyright Embark on the Journey

Terms of Use. Copyright Embark on the Journey Terms of Use All rights reserved. No part of this packet may be reproduced, stored in a retrieval system, or transmitted in any form by any means - electronic, mechanical, photo-copies, recording, or otherwise

More information

Thomas J. Botzman, Ph.D. President. President s Message 2. Official Color Palette 3. The Logo 4. The Icon 7. The Wordmark 10

Thomas J. Botzman, Ph.D. President. President s Message 2. Official Color Palette 3. The Logo 4. The Icon 7. The Wordmark 10 Graphic Standards Manual Misericordia University PRESIDENT S MESSAGE This graphic standards manual introduces and explains Misericordia s visual identity and institutional brand. The consistent use of

More information

Our Identity. A basic manual of standards. Version 1.0 April Laureate Education, Inc.

Our Identity. A basic manual of standards. Version 1.0 April Laureate Education, Inc. Our Identity A basic manual of standards Version 1.0 April 2010 2010 Laureate Education, Inc. TA B L E O F C O N T E N T S Part 1 - Welcome 3 Shaping relationships 4 Laureate International Universities

More information

A A A A A A A A A A A A. a a a a a a a a a a a a a a a. Apples taste amazingly good.

A A A A A A A A A A A A. a a a a a a a a a a a a a a a. Apples taste amazingly good. Victorian Handwriting Sheet Aa A A A A A A A A A A A A Aa Aa Aa Aa Aa Aa Aa a a a a a a a a a a a a a a a Apples taste amazingly good. Apples taste amazingly good. Now make up a sentence of your own using

More information

Worksheets for GCSE Mathematics. Quadratics. mr-mathematics.com Maths Resources for Teachers. Algebra

Worksheets for GCSE Mathematics. Quadratics. mr-mathematics.com Maths Resources for Teachers. Algebra Worksheets for GCSE Mathematics Quadratics mr-mathematics.com Maths Resources for Teachers Algebra Quadratics Worksheets Contents Differentiated Independent Learning Worksheets Solving x + bx + c by factorisation

More information

1. The graph of a function f is given above. Answer the question: a. Find the value(s) of x where f is not differentiable. Ans: x = 4, x = 3, x = 2,

1. The graph of a function f is given above. Answer the question: a. Find the value(s) of x where f is not differentiable. Ans: x = 4, x = 3, x = 2, 1. The graph of a function f is given above. Answer the question: a. Find the value(s) of x where f is not differentiable. x = 4, x = 3, x = 2, x = 1, x = 1, x = 2, x = 3, x = 4, x = 5 b. Find the value(s)

More information

Appendix A. Brand. Guidelines

Appendix A. Brand. Guidelines Appendix A Brand Guidelines Primary Logos These are the two primary logos. We have a centred and a left aligned version for ease of use. It is essential that the logo always be applied with care in every

More information

EnOcean Alliance Brand Guidelines

EnOcean Alliance Brand Guidelines EnOcean Alliance Brand Guidelines V 2.0, Jan 2017 2017 EnOcean Alliance www.enocean-alliance.org 1/21 EnOcean Alliance The EnOcean Alliance is a is a consortium of companies working to further develop

More information

Brand guidelines 2014

Brand guidelines 2014 Brand guidelines 2014 // master logo // master logo & alternative colour breakdowns Blue C: 100 M: 95 Y: 5 K: 0 R: 43 G: 57 B: 144 #2b3990 // master logo - alternate colourful version // master logo -

More information

Patterns of soiling in the Old Library Trinity College Dublin. Allyson Smith, Robbie Goodhue, Susie Bioletti

Patterns of soiling in the Old Library Trinity College Dublin. Allyson Smith, Robbie Goodhue, Susie Bioletti Patterns of soiling in the Old Library Trinity College Dublin Allyson Smith, Robbie Goodhue, Susie Bioletti Trinity College aerial view Old Library E N S W Old Library main (south) elevation Gallery Fagel

More information

SECTION 7: STEADY-STATE ERROR. ESE 499 Feedback Control Systems

SECTION 7: STEADY-STATE ERROR. ESE 499 Feedback Control Systems SECTION 7: STEADY-STATE ERROR ESE 499 Feedback Control Systems 2 Introduction Steady-State Error Introduction 3 Consider a simple unity-feedback system The error is the difference between the reference

More information

Secondary 3H Unit = 1 = 7. Lesson 3.3 Worksheet. Simplify: Lesson 3.6 Worksheet

Secondary 3H Unit = 1 = 7. Lesson 3.3 Worksheet. Simplify: Lesson 3.6 Worksheet Secondary H Unit Lesson Worksheet Simplify: mm + 2 mm 2 4 mm+6 mm + 2 mm 2 mm 20 mm+4 5 2 9+20 2 0+25 4 +2 2 + 2 8 2 6 5. 2 yy 2 + yy 6. +2 + 5 2 2 2 0 Lesson 6 Worksheet List all asymptotes, holes and

More information

Classification of Components

Classification of Components Classification of Components Classification of SMD LEDs TLM.31../TLM.32../TLM.33../ + 3... series, Mini LEDs TLM.21... / TLM.23.. / TLM.2.. and 63 LEDs TLM.11../TLM1.. Light Intensity / Color Devices are

More information

General Strong Polarization

General Strong Polarization General Strong Polarization Madhu Sudan Harvard University Joint work with Jaroslaw Blasiok (Harvard), Venkatesan Gurswami (CMU), Preetum Nakkiran (Harvard) and Atri Rudra (Buffalo) December 4, 2017 IAS:

More information

" = Y(#,$) % R(r) = 1 4& % " = Y(#,$) % R(r) = Recitation Problems: Week 4. a. 5 B, b. 6. , Ne Mg + 15 P 2+ c. 23 V,

 = Y(#,$) % R(r) = 1 4& %  = Y(#,$) % R(r) = Recitation Problems: Week 4. a. 5 B, b. 6. , Ne Mg + 15 P 2+ c. 23 V, Recitation Problems: Week 4 1. Which of the following combinations of quantum numbers are allowed for an electron in a one-electron atom: n l m l m s 2 2 1! 3 1 0 -! 5 1 2! 4-1 0! 3 2 1 0 2 0 0 -! 7 2-2!

More information

Worksheets for GCSE Mathematics. Algebraic Expressions. Mr Black 's Maths Resources for Teachers GCSE 1-9. Algebra

Worksheets for GCSE Mathematics. Algebraic Expressions. Mr Black 's Maths Resources for Teachers GCSE 1-9. Algebra Worksheets for GCSE Mathematics Algebraic Expressions Mr Black 's Maths Resources for Teachers GCSE 1-9 Algebra Algebraic Expressions Worksheets Contents Differentiated Independent Learning Worksheets

More information

Quantitative Screening of 46 Illicit Drugs in Urine using Exactive Ultrahigh Resolution and Accurate Mass system

Quantitative Screening of 46 Illicit Drugs in Urine using Exactive Ultrahigh Resolution and Accurate Mass system Quantitative Screening of 46 Illicit Drugs in Urine using Exactive Ultrahigh Resolution and Accurate Mass system Kevin Mchale Thermo Fisher Scientific, San Jose CA Presentation Overview Anabolic androgenic

More information

TSOKOS READING ACTIVITY Section 7-2: The Greenhouse Effect and Global Warming (8 points)

TSOKOS READING ACTIVITY Section 7-2: The Greenhouse Effect and Global Warming (8 points) IB PHYSICS Name: Period: Date: DEVIL PHYSICS BADDEST CLASS ON CAMPUS TSOKOS READING ACTIVITY Section 7-2: The Greenhouse Effect and Global Warming (8 points) 1. IB Assessment Statements for Topic 8.5.

More information

Big Bang Planck Era. This theory: cosmological model of the universe that is best supported by several aspects of scientific evidence and observation

Big Bang Planck Era. This theory: cosmological model of the universe that is best supported by several aspects of scientific evidence and observation Big Bang Planck Era Source: http://www.crystalinks.com/bigbang.html Source: http://www.odec.ca/index.htm This theory: cosmological model of the universe that is best supported by several aspects of scientific

More information

Uncertain Compression & Graph Coloring. Madhu Sudan Harvard

Uncertain Compression & Graph Coloring. Madhu Sudan Harvard Uncertain Compression & Graph Coloring Madhu Sudan Harvard Based on joint works with: (1) Adam Kalai (MSR), Sanjeev Khanna (U.Penn), Brendan Juba (WUStL) (2) Elad Haramaty (Harvard) (3) Badih Ghazi (MIT),

More information

10.4 The Cross Product

10.4 The Cross Product Math 172 Chapter 10B notes Page 1 of 9 10.4 The Cross Product The cross product, or vector product, is defined in 3 dimensions only. Let aa = aa 1, aa 2, aa 3 bb = bb 1, bb 2, bb 3 then aa bb = aa 2 bb

More information

Mathematical Methods 2019 v1.2

Mathematical Methods 2019 v1.2 Problem-solving and modelling task (20%) This sample has been compiled by the QCAA to assist and support teachers to match evidence in student responses to the characteristics described in the instrument-specific

More information

Math 95--Review Prealgebra--page 1

Math 95--Review Prealgebra--page 1 Math 95--Review Prealgebra--page 1 Name Date In order to do well in algebra, there are many different ideas from prealgebra that you MUST know. Some of the main ideas follow. If these ideas are not just

More information

Harlean. User s Guide

Harlean. User s Guide Harlean User s Guide font faq HOW TO INSTALL YOUR FONT You will receive your files as a zipped folder. For instructions on how to unzip your folder, visit LauraWorthingtonType.com/faqs/. Your font is available

More information

How to use this catalog

How to use this catalog Font Catalog Copyright 2005 Vision Engraving Systems. All rights reserved. This publication is protected by copyright, and all rights are reserved. No part of this manual may be reproduced or transmitted

More information

Style & Branding Guide

Style & Branding Guide Style & Branding Guide 10.10. 2010 Style & Branding Guide 10.10. 2010 Welcome, Fellow human to the unique little world of SEOmoz brand awareness and usage. In this guide you will find guidelines for the

More information

Chapter 22 : Electric potential

Chapter 22 : Electric potential Chapter 22 : Electric potential What is electric potential? How does it relate to potential energy? How does it relate to electric field? Some simple applications What does it mean when it says 1.5 Volts

More information

6 Lowercase Letter a Number Puzzles

6 Lowercase Letter a Number Puzzles 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 70 80 90 100 6 Lowercase Letter a Nuber Puzzles 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1

More information

Work, Energy, and Power. Chapter 6 of Essential University Physics, Richard Wolfson, 3 rd Edition

Work, Energy, and Power. Chapter 6 of Essential University Physics, Richard Wolfson, 3 rd Edition Work, Energy, and Power Chapter 6 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 With the knowledge we got so far, we can handle the situation on the left but not the one on the right.

More information

UltraWeatherBug3 HSPI User s Guide A HomeSeer HS3 plug-in to access live local weather conditions, forecasts and severe weather alerts

UltraWeatherBug3 HSPI User s Guide A HomeSeer HS3 plug-in to access live local weather conditions, forecasts and severe weather alerts UltraWeatherBug3 HSPI User s Guide A HomeSeer HS3 plug-in to access live local weather conditions, forecasts and severe weather alerts Copyright 2015 ultrajones@hotmail.com Revised 08/08/2015 This document

More information

Lecture 11. Kernel Methods

Lecture 11. Kernel Methods Lecture 11. Kernel Methods COMP90051 Statistical Machine Learning Semester 2, 2017 Lecturer: Andrey Kan Copyright: University of Melbourne This lecture The kernel trick Efficient computation of a dot product

More information

Charge carrier density in metals and semiconductors

Charge carrier density in metals and semiconductors Charge carrier density in metals and semiconductors 1. Introduction The Hall Effect Particles must overlap for the permutation symmetry to be relevant. We saw examples of this in the exchange energy in

More information

Lesson 7: Linear Transformations Applied to Cubes

Lesson 7: Linear Transformations Applied to Cubes Classwork Opening Exercise Consider the following matrices: AA = 1 2 0 2, BB = 2, and CC = 2 2 4 0 0 2 2 a. Compute the following determinants. i. det(aa) ii. det(bb) iii. det(cc) b. Sketch the image of

More information

General Strong Polarization

General Strong Polarization General Strong Polarization Madhu Sudan Harvard University Joint work with Jaroslaw Blasiok (Harvard), Venkatesan Gurswami (CMU), Preetum Nakkiran (Harvard) and Atri Rudra (Buffalo) May 1, 018 G.Tech:

More information

Systems of Linear Equations

Systems of Linear Equations Systems of Linear Equations As stated in Section G, Definition., a linear equation in two variables is an equation of the form AAAA + BBBB = CC, where AA and BB are not both zero. Such an equation has

More information

Specialist Mathematics 2019 v1.2

Specialist Mathematics 2019 v1.2 Examination (15%) This sample has been compiled by the QCAA to assist and support teachers in planning and developing assessment instruments for individual school settings. The examination must ensure

More information

Lesson 24: True and False Number Sentences

Lesson 24: True and False Number Sentences NYS COMMON CE MATHEMATICS CURRICULUM Lesson 24 6 4 Student Outcomes Students identify values for the variables in equations and inequalities that result in true number sentences. Students identify values

More information

Vero Beach Elks Lodge # th Street Vero Beach, FL /

Vero Beach Elks Lodge # th Street Vero Beach, FL / 1350-26th Street Vero Beach, FL 32960 772/562-8450 Annual Harry-Anna Saturday, February 13, 2016 Featuring our Popular Roast Beef Dinner Potatoes, Corn-on-the-Cob, Salad & Dessert by Chef Vic Cocktails:

More information

T ING S ADV E C T L IVE N A T I O N A L J A M B O R E E N N S E S C O U T S N A A L JA M B

T ING S ADV E C T L IVE N A T I O N A L J A M B O R E E N N S E S C O U T S N A A L JA M B S ING S AD VE N C T OU RE L IVE TU RE S C O U T S O F A M E R I C A G U I D E L I N E S 2 0 1 7 P A C K A G E / N A T I O N A L J U l y 9, J A M B O R E E 2 0 1 5 OU T ING S ADV E N C TU RE N A TI E E

More information

SECTION 7: FAULT ANALYSIS. ESE 470 Energy Distribution Systems

SECTION 7: FAULT ANALYSIS. ESE 470 Energy Distribution Systems SECTION 7: FAULT ANALYSIS ESE 470 Energy Distribution Systems 2 Introduction Power System Faults 3 Faults in three-phase power systems are short circuits Line-to-ground Line-to-line Result in the flow

More information

Support Vector Machines. CSE 4309 Machine Learning Vassilis Athitsos Computer Science and Engineering Department University of Texas at Arlington

Support Vector Machines. CSE 4309 Machine Learning Vassilis Athitsos Computer Science and Engineering Department University of Texas at Arlington Support Vector Machines CSE 4309 Machine Learning Vassilis Athitsos Computer Science and Engineering Department University of Texas at Arlington 1 A Linearly Separable Problem Consider the binary classification

More information

Preparation of Optically Pure Tertiary Phosphine Oxides via Addition of P-Stereogenic Secondary Phosphine Oxide to Activated Alkenes

Preparation of Optically Pure Tertiary Phosphine Oxides via Addition of P-Stereogenic Secondary Phosphine Oxide to Activated Alkenes Preparation of Optically Pure Tertiary Phosphine Oxides via Addition of P-Stereogenic Secondary Phosphine Oxide to Activated Alkenes Ji-Ping Wang, Shao-Zhen Nie, Zhong-Yang Zhou, Jing-Jing Ye, Jing-Hong

More information

Thermodynamic Cycles

Thermodynamic Cycles Thermodynamic Cycles Content Thermodynamic Cycles Carnot Cycle Otto Cycle Rankine Cycle Refrigeration Cycle Thermodynamic Cycles Carnot Cycle Derivation of the Carnot Cycle Efficiency Otto Cycle Otto Cycle

More information

Module 7 (Lecture 27) RETAINING WALLS

Module 7 (Lecture 27) RETAINING WALLS Module 7 (Lecture 27) RETAINING WALLS Topics 1.1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT Calculation of Active Horizontal and vertical Pressure Tie Force Factor of Safety Against Tie Failure

More information

Heat, Work, and the First Law of Thermodynamics. Chapter 18 of Essential University Physics, Richard Wolfson, 3 rd Edition

Heat, Work, and the First Law of Thermodynamics. Chapter 18 of Essential University Physics, Richard Wolfson, 3 rd Edition Heat, Work, and the First Law of Thermodynamics Chapter 18 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 Different ways to increase the internal energy of system: 2 Joule s apparatus

More information

Lecture No. 1 Introduction to Method of Weighted Residuals. Solve the differential equation L (u) = p(x) in V where L is a differential operator

Lecture No. 1 Introduction to Method of Weighted Residuals. Solve the differential equation L (u) = p(x) in V where L is a differential operator Lecture No. 1 Introduction to Method of Weighted Residuals Solve the differential equation L (u) = p(x) in V where L is a differential operator with boundary conditions S(u) = g(x) on Γ where S is a differential

More information

Section 2: Equations and Inequalities

Section 2: Equations and Inequalities Topic 1: Equations: True or False?... 29 Topic 2: Identifying Properties When Solving Equations... 31 Topic 3: Solving Equations... 34 Topic 4: Solving Equations Using the Zero Product Property... 36 Topic

More information

Quantum Mechanics. An essential theory to understand properties of matter and light. Chemical Electronic Magnetic Thermal Optical Etc.

Quantum Mechanics. An essential theory to understand properties of matter and light. Chemical Electronic Magnetic Thermal Optical Etc. Quantum Mechanics An essential theory to understand properties of matter and light. Chemical Electronic Magnetic Thermal Optical Etc. Fall 2018 Prof. Sergio B. Mendes 1 CHAPTER 3 Experimental Basis of

More information

Locality in Coding Theory

Locality in Coding Theory Locality in Coding Theory Madhu Sudan Harvard April 9, 2016 Skoltech: Locality in Coding Theory 1 Error-Correcting Codes (Linear) Code CC FF qq nn. FF qq : Finite field with qq elements. nn block length

More information

Guide to Chapter 15. Aqueous Equilibria: Acids and Bases. Review Chapter 4, Section 2 on how ionic substances dissociate in water.

Guide to Chapter 15. Aqueous Equilibria: Acids and Bases. Review Chapter 4, Section 2 on how ionic substances dissociate in water. Guide to Chapter 15. Aqueous Equilibria: Acids and Bases We will spend five lecture days on this chapter. During the first two class meetings we will introduce acids and bases and some of the theories

More information

TECHNICAL NOTE AUTOMATIC GENERATION OF POINT SPRING SUPPORTS BASED ON DEFINED SOIL PROFILES AND COLUMN-FOOTING PROPERTIES

TECHNICAL NOTE AUTOMATIC GENERATION OF POINT SPRING SUPPORTS BASED ON DEFINED SOIL PROFILES AND COLUMN-FOOTING PROPERTIES COMPUTERS AND STRUCTURES, INC., FEBRUARY 2016 TECHNICAL NOTE AUTOMATIC GENERATION OF POINT SPRING SUPPORTS BASED ON DEFINED SOIL PROFILES AND COLUMN-FOOTING PROPERTIES Introduction This technical note

More information

CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I

CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I 1 5.1 X-Ray Scattering 5.2 De Broglie Waves 5.3 Electron Scattering 5.4 Wave Motion 5.5 Waves or Particles 5.6 Uncertainty Principle Topics 5.7

More information

National Science Olympiad 2014 Division B: Solar System May 17th 2014

National Science Olympiad 2014 Division B: Solar System May 17th 2014 National Science Olympiad 2014 Division B: Solar System May 17th 2014 Sponsored by the University of Texas Institute for Geophysics Team Number: Team Name: Questions 1-24 refer to the images in Image Set

More information

Acceleration due to Gravity

Acceleration due to Gravity 1. Object Acceleration due to Gravity To determine the acceleration due to gravity by different methods. 2. Apparatus Balance, ball bearing, clamps, electric timers, meter stick, paper strips, precision

More information

A A. an at and April fat Ana black orange gray cage. A a A a a f A a g A N a A n N p A G a A g A n a A a a A g a. Name. Copy the letter Aa.

A A. an at and April fat Ana black orange gray cage. A a A a a f A a g A N a A n N p A G a A g A n a A a a A g a. Name. Copy the letter Aa. Copy the letter Aa. A A a a Highlight the letter Aa. an at and April that fat Ana black orange gray cage Glue the uppercase A here. Glue the lowercase a here. A a A a a f A a g A N a A n N p A G a A g

More information

Review for Exam Hyunse Yoon, Ph.D. Assistant Research Scientist IIHR-Hydroscience & Engineering University of Iowa

Review for Exam Hyunse Yoon, Ph.D. Assistant Research Scientist IIHR-Hydroscience & Engineering University of Iowa 57:020 Fluids Mechanics Fall2013 1 Review for Exam3 12. 11. 2013 Hyunse Yoon, Ph.D. Assistant Research Scientist IIHR-Hydroscience & Engineering University of Iowa 57:020 Fluids Mechanics Fall2013 2 Chapter

More information

Aa Bb Cc Dd. Ee Ff Gg Hh

Aa Bb Cc Dd. Ee Ff Gg Hh Aa Bb Cc Dd ------------------------------------------------------------------------------------------------------------------------------------------------------- Ee Ff Gg Hh -------------------------------------------------------------------------------------------------------------------------------------------------------

More information

Gravitation. Chapter 8 of Essential University Physics, Richard Wolfson, 3 rd Edition

Gravitation. Chapter 8 of Essential University Physics, Richard Wolfson, 3 rd Edition Gravitation Chapter 8 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 What you are about to learn: Newton's law of universal gravitation About motion in circular and other orbits How to

More information

Genetics Review Sheet Learning Target 11: Explain where and how an organism inherits its genetic information and this influences their

Genetics Review Sheet Learning Target 11: Explain where and how an organism inherits its genetic information and this influences their Genetics Review Sheet Learning Target 11: Explain where and how an organism inherits its genetic information and this influences their characteristics. 1. Define the following terms: Name Block a. Heredity

More information

Introduction to Electrical Theory and DC Circuits

Introduction to Electrical Theory and DC Circuits Introduction to Electrical Theory and DC Circuits For Engineers of All Disciplines by James Doane, PhD, PE Contents 1.0 Course Overview... 4 2.0 Fundamental Concepts... 4 2.1 Electric Charges... 4 2.1.1

More information

Rotational Motion. Chapter 10 of Essential University Physics, Richard Wolfson, 3 rd Edition

Rotational Motion. Chapter 10 of Essential University Physics, Richard Wolfson, 3 rd Edition Rotational Motion Chapter 10 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 We ll look for a way to describe the combined (rotational) motion 2 Angle Measurements θθ ss rr rrrrrrrrrrrrrr

More information

children's illustrator

children's illustrator th, The summer before kindergarten is so exciting. This packet was designed to give you insight in to the different activities you can do with your child. After completing a worksheet, you have an idea

More information

Winsome Winsome W Wins e ins e WUin ser some s Guide

Winsome Winsome W Wins e ins e WUin ser some s Guide Winsome Winsome Wins e Wins e U ser s Guide Winsome font faq HOW TO INSTALL YOUR FONT You will receive your files as a zipped folder. For instructions on how to unzip your folder, visit LauraWorthingtonType.com/faqs/.

More information

SECTION 8: ROOT-LOCUS ANALYSIS. ESE 499 Feedback Control Systems

SECTION 8: ROOT-LOCUS ANALYSIS. ESE 499 Feedback Control Systems SECTION 8: ROOT-LOCUS ANALYSIS ESE 499 Feedback Control Systems 2 Introduction Introduction 3 Consider a general feedback system: Closed-loop transfer function is KKKK ss TT ss = 1 + KKKK ss HH ss GG ss

More information

Revision : Thermodynamics

Revision : Thermodynamics Revision : Thermodynamics Formula sheet Formula sheet Formula sheet Thermodynamics key facts (1/9) Heat is an energy [measured in JJ] which flows from high to low temperature When two bodies are in thermal

More information

Brand Standards & Packaging Style Guide

Brand Standards & Packaging Style Guide Brand Standards & Packaging Style Guide Table of Contents Introduction....................................................... 3 Black Magic Logo Approved Usage.................................................

More information

allosteric cis-acting DNA element coding strand dominant constitutive mutation coordinate regulation of genes denatured

allosteric cis-acting DNA element coding strand dominant constitutive mutation coordinate regulation of genes denatured A B C D E F G H I J K L M N O P Q R S T U V W X Y Z AA BB CC DD EE FF GG HH II JJ KK LL MM NN OO PP QQ RR SS TT UU VV allosteric cis-acting DNA element coding strand codominant constitutive mutation coordinate

More information

QJ) Zz LI Zz. Dd Jj. Jj Ww J' J Ww. Jj Ww. Jj I\~~ SOUN,DS AND LETTERS

QJ) Zz LI Zz. Dd Jj. Jj Ww J' J Ww. Jj Ww. Jj I\~~ SOUN,DS AND LETTERS SOUN,DS AND LETTERS.--< Say the name of each picture.llsten to the first sound. Then circle the letters with that"sound..-.. Dd QJ) Jj Ww J' J Ww Zz LI Zz Dd Jj Ww Dd Jj Zz Jj LI Ww Jj LI Ww Jj Ww Zz Dd

More information

T A B L E O F C O N T E N T S

T A B L E O F C O N T E N T S CHADWICK DOLPHINS LOGO STYLE GUIDE T A B L E O F C O N T E N T S 3 Letter From the Headmaster 4 Basic Guidelines For Use 5 Logo Anatomy 6 The Pacific Dolphin 7 Logo Color 8 Color Specifications 9 Typeface

More information

CHAPTER 2 Special Theory of Relativity

CHAPTER 2 Special Theory of Relativity CHAPTER 2 Special Theory of Relativity Fall 2018 Prof. Sergio B. Mendes 1 Topics 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 Inertial Frames of Reference Conceptual and Experimental

More information

CLEAR SPACE AND MINIMUM SIZE. A clear space area free of competing visual elements should be maintained.

CLEAR SPACE AND MINIMUM SIZE. A clear space area free of competing visual elements should be maintained. BRAND TOOL KIT LOGO The preferred logoversion to use is on white background. Negative version is reversed (white) on a dark blue background. Also a black and white version is available for 1-colour print

More information

FTEJerez Corporate Identity Brand Guidelines. Version 2015

FTEJerez Corporate Identity Brand Guidelines. Version 2015 FTEJerez Corporate Identity Brand Guidelines Version 2015 Brand rules These guidelines specify the correct use of FTEJerez corporate elements such as logotype, imagotype or variations of the same. Our

More information

Lesson 10: Solving Inequalities

Lesson 10: Solving Inequalities Opening Exercise 1. Find the solution set to each inequality. Express the solution graphically on the number line and give the solution in interval notation. A. xx + 4 7 B. mm 3 + 8 > 9 C. 8yy + 4 < 7yy

More information

Model answers for the 2012 Electricity Revision booklet:

Model answers for the 2012 Electricity Revision booklet: Model answers for the 0 Electricity Revision booklet: SAMPLE ASSESSMENT SCHEDULE Physics 973 (.6): Demonstrate understanding of electricity and electromagnetism Assessment Criteria Achievement Achievement

More information

Math 171 Spring 2017 Final Exam. Problem Worth

Math 171 Spring 2017 Final Exam. Problem Worth Math 171 Spring 2017 Final Exam Problem 1 2 3 4 5 6 7 8 9 10 11 Worth 9 6 6 5 9 8 5 8 8 8 10 12 13 14 15 16 17 18 19 20 21 22 Total 8 5 5 6 6 8 6 6 6 6 6 150 Last Name: First Name: Student ID: Section:

More information

one brand. one face. one voice.

one brand. one face. one voice. one brand. one face. one voice. In essence, brand guidelines are a set of rules followed by the company to maintain the brand s identity. They play an indispensable part in the overall representation of

More information

Study on Flow Characteristics of Oil Viscosity Pump for Refrigerant Compressors

Study on Flow Characteristics of Oil Viscosity Pump for Refrigerant Compressors Purdue University Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 2016 Study on Flow Characteristics of Oil Viscosity Pump for Refrigerant Compressors Kiyoshi

More information

Large Scale Data Analysis Using Deep Learning

Large Scale Data Analysis Using Deep Learning Large Scale Data Analysis Using Deep Learning Linear Algebra U Kang Seoul National University U Kang 1 In This Lecture Overview of linear algebra (but, not a comprehensive survey) Focused on the subset

More information

Estimate by the L 2 Norm of a Parameter Poisson Intensity Discontinuous

Estimate by the L 2 Norm of a Parameter Poisson Intensity Discontinuous Research Journal of Mathematics and Statistics 6: -5, 24 ISSN: 242-224, e-issn: 24-755 Maxwell Scientific Organization, 24 Submied: September 8, 23 Accepted: November 23, 23 Published: February 25, 24

More information

Äppelkärnan brandbook

Äppelkärnan brandbook Äppelkärnan brandbook O2 INDEX 03/ GOALS AND MISSION LOGOTYPE 04/ principal logotype 05/ secondary logotype 06/ TYPOGRAPHY principal and secondary COLOUR 07/ CMYK,RGB, WEB 08/ colour version 09-012/ colour

More information

English 1 Name:

English 1 Name: English 1 Name: 2A 2014-2015 English 1 Name: 2B 2014-2015 Alphabet Aa (ei) Bb (bi) Cc (si) Dd (di) Ee (i) Ff (ef) Gg (lli) Hh (eich) Ii (ai) Jj (llei) Kk (quei) Ll (el) Mm (em) Nn (en) Oo (Ou) Pp (pi)

More information

Recurrence Relations

Recurrence Relations Recurrence Relations Recurrence Relations Reading (Epp s textbook) 5.6 5.8 1 Recurrence Relations A recurrence relation for a sequence aa 0, aa 1, aa 2, ({a n }) is a formula that relates each term a k

More information

Haar Basis Wavelets and Morlet Wavelets

Haar Basis Wavelets and Morlet Wavelets Haar Basis Wavelets and Morlet Wavelets September 9 th, 05 Professor Davi Geiger. The Haar transform, which is one of the earliest transform functions proposed, was proposed in 90 by a Hungarian mathematician

More information

Lecture No. 5. For all weighted residual methods. For all (Bubnov) Galerkin methods. Summary of Conventional Galerkin Method

Lecture No. 5. For all weighted residual methods. For all (Bubnov) Galerkin methods. Summary of Conventional Galerkin Method Lecture No. 5 LL(uu) pp(xx) = 0 in ΩΩ SS EE (uu) = gg EE on ΓΓ EE SS NN (uu) = gg NN on ΓΓ NN For all weighted residual methods NN uu aaaaaa = uu BB + αα ii φφ ii For all (Bubnov) Galerkin methods ii=1

More information

Math 3 Unit 4: Rational Functions

Math 3 Unit 4: Rational Functions Math Unit : Rational Functions Unit Title Standards. Equivalent Rational Expressions A.APR.6. Multiplying and Dividing Rational Expressions A.APR.7. Adding and Subtracting Rational Expressions A.APR.7.

More information

IBU VENUE DRESSING GUIDE IBU VENUE DRESSING GUIDE IBU JUNIOR CUP BIATHLON. (IBU Brand Identification for Biathlon Venues) IBU Junior Cup Biathlon

IBU VENUE DRESSING GUIDE IBU VENUE DRESSING GUIDE IBU JUNIOR CUP BIATHLON. (IBU Brand Identification for Biathlon Venues) IBU Junior Cup Biathlon IBU (IBU Brand Identification for Biathlon Venues) IBU Junior Cup Biathlon (Without live TV coverage) Effective from season 2018/2019 IBU 1 PREAMBLE The new IBU Branding IBU, the International Biathlon

More information

Review of Last Class 1

Review of Last Class 1 Review of Last Class 1 X-Ray diffraction of crystals: the Bragg formulation Condition of diffraction peak: 2dd sin θθ = nnλλ Review of Last Class 2 X-Ray diffraction of crystals: the Von Laue formulation

More information

Control of Mobile Robots

Control of Mobile Robots Control of Mobile Robots Regulation and trajectory tracking Prof. Luca Bascetta (luca.bascetta@polimi.it) Politecnico di Milano Dipartimento di Elettronica, Informazione e Bioingegneria Organization and

More information

F.4 Solving Polynomial Equations and Applications of Factoring

F.4 Solving Polynomial Equations and Applications of Factoring section F4 243 F.4 Zero-Product Property Many application problems involve solving polynomial equations. In Chapter L, we studied methods for solving linear, or first-degree, equations. Solving higher

More information

CHAPTER 4 Structure of the Atom

CHAPTER 4 Structure of the Atom CHAPTER 4 Structure of the Atom Fall 2018 Prof. Sergio B. Mendes 1 Topics 4.1 The Atomic Models of Thomson and Rutherford 4.2 Rutherford Scattering 4.3 The Classic Atomic Model 4.4 The Bohr Model of the

More information

Aa Bb Cc Dd. Ee Ff Gg Hh

Aa Bb Cc Dd. Ee Ff Gg Hh Aa Bb Cc Dd ------------------------------------------------------------------------------------------------------------------------------------------------------- Ee Ff Gg Hh -------------------------------------------------------------------------------------------------------------------------------------------------------

More information

Lecture 6. Notes on Linear Algebra. Perceptron

Lecture 6. Notes on Linear Algebra. Perceptron Lecture 6. Notes on Linear Algebra. Perceptron COMP90051 Statistical Machine Learning Semester 2, 2017 Lecturer: Andrey Kan Copyright: University of Melbourne This lecture Notes on linear algebra Vectors

More information

Eureka Lessons for 6th Grade Unit FIVE ~ Equations & Inequalities

Eureka Lessons for 6th Grade Unit FIVE ~ Equations & Inequalities Eureka Lessons for 6th Grade Unit FIVE ~ Equations & Inequalities These 2 lessons can easily be taught in 2 class periods. If you like these lessons, please consider using other Eureka lessons as well.

More information

L.2 Formulas and Applications

L.2 Formulas and Applications 43 L. Formulas and Applications In the previous section, we studied how to solve linear equations. Those skills are often helpful in problem solving. However, the process of solving an application problem

More information

7.3 The Jacobi and Gauss-Seidel Iterative Methods

7.3 The Jacobi and Gauss-Seidel Iterative Methods 7.3 The Jacobi and Gauss-Seidel Iterative Methods 1 The Jacobi Method Two assumptions made on Jacobi Method: 1.The system given by aa 11 xx 1 + aa 12 xx 2 + aa 1nn xx nn = bb 1 aa 21 xx 1 + aa 22 xx 2

More information

Worksheets for GCSE Mathematics. Solving Equations. Mr Black's Maths Resources for Teachers GCSE 1-9. Algebra

Worksheets for GCSE Mathematics. Solving Equations. Mr Black's Maths Resources for Teachers GCSE 1-9. Algebra Worksheets for GCSE Mathematics Solving Equations Mr Black's Maths Resources for Teachers GCSE 1-9 Algebra Equations Worksheets Contents Differentiated Independent Learning Worksheets Solving Equations

More information

Rational Equations and Graphs

Rational Equations and Graphs RT.5 Rational Equations and Graphs Rational Equations In previous sections of this chapter, we worked with rational expressions. If two rational expressions are equated, a rational equation arises. Such

More information

Grover s algorithm. We want to find aa. Search in an unordered database. QC oracle (as usual) Usual trick

Grover s algorithm. We want to find aa. Search in an unordered database. QC oracle (as usual) Usual trick Grover s algorithm Search in an unordered database Example: phonebook, need to find a person from a phone number Actually, something else, like hard (e.g., NP-complete) problem 0, xx aa Black box ff xx

More information

Classwork. Example 1 S.35

Classwork. Example 1 S.35 Classwork Example 1 In the picture below, we have a triangle AAAAAA that has been dilated from center OO by a scale factor of rr = 1. It is noted 2 by AA BB CC. We also have triangle AA BB CC, which is

More information