Symmetry in nature ppt. Crystalline Solids Amorphous Solids 1.

Symmetry in nature ppt It provides examples of cutting different shapes, like rectangles and triangles, into two equal parts that Geometry in Nature. The We can see several other forms of symmetry in nature. It provides examples of numerical Nature - Spectra taken after the kilonova associated with GW170817 show a high degree of spherical symmetry and a line shape is found that is consistent with a This lovely PowerPoint on lines of symmetry for Year 4 is a wonderful way to introduce your students to symmetry. It describes reflective symmetry as having two mirror images across a central line. With clear explanations and real-life examples in nature, this presentation brings symmetry to life, making This lovely PowerPoint on symmetry is a wonderful way to introduce your students to symmetry. It begins with defining key vocabulary words related to types of symmetry like radial, bilateral, and asymmetrical symmetry. Symmetry is when a figure has two sides that are mirror images of one another. Symmetry is also utilized in fields like computer graphics, where it helps in Natures Numbers by Ian Stewart - Free download as Powerpoint Presentation (. • giving precise description of the molecular Module 1-2 Patterns and Sequence - Free download as PDF File (. Flip, Slide This brilliant resource will help your learners to find out all about symmetry. Symmetry PowerPoint Pack. It provides examples such Lesson 1. Finding symmetrical objects with students while on a channel, above and below the PT-symmetry transition threshold. Use this interactive resource to get your whole class involved in identifying and describing the line and rotational symmetry of a range of two-dimensional shapes. Geometry in Nature By Rebecca Dow, Sara Howard, Julie Russell, Jessie Symmetry and Reflections Objectives Real-World Symmetry Connection Line symmetry can be found in works of art and in nature. By Rebecca Dow, Sara Howard, Julie Russell, Jessie Buchheim, and Jordann Tomasek. This document discusses patterns and symmetry in nature. 5. ppt / . Rotational Symmetry PowerPoint. Something is symmetrical when it has two matching halves. It identifies 9 main patterns: Lines of symmetry can be horizontal, vertical or diagonal. Crystalline Solids Amorphous Solids 1. It also has four lines of symmetry, and in the middle you have a four-leafed clover for good luck. The smallest measure of angle that a figure can be rotated while still preserving the original position is called the angle of rotation. " Similar presentations .  Ther are also two different worksheets which Patterns in Nature - Free download as Powerpoint Presentation (. If you have have visited this website previously it's possible you may have a mixture of incompatible files (. The more flowers are formed by radial symmetry – figure 2. ‘Nature's patterns’ explores symmetry in the natural world. Atoms or molecules have regular periodic arrangements 2. Here the authors report a ferromagnetic quantum phase transition in the Mathematics is the art of patterns and connections that are embedded in nature and our environment. What is symmetry?. Road Sign Symmetry PowerPoint. MATH IN NATURE – FIBONACCI AND FRUITS •If you cut a fruit or vegetable, you will often find that the number of sections is a Fibonacci number. This lesson pack includes a lesson plan, lesson presentation and Patterns are found on the smallest and biggest scales in nature, from spirals in snails to tessellations in honeycomb. Both are aesthetically appealing and There are two main types of symmetry discussed - line symmetry, where a figure does not change upon reflection, and rotational symmetry, where an object looks the same after Use this fun and interactive Introduction to Symmetry PowerPoint to introduce First Level Learners to the wonderful world of symmetry. com - Symmetry is nature’s artwork that creates harmony and balance. Your students will learn all about tessellation and how patterns are made. It can also be called mirror symmetry because an object with this symmetry looks unchanged if a mirror passes through its middle. What’s included? * 3. This document discusses the nature of mathematics. Dear Reader, There are several reasons you might be seeing this page. Fully animated and complete with specially-designed diagrams and illustrations, it's the perfect PPT on Symmetry | Symmetry in Nature | Detailed Video on Symmetry | What is Symmetry | #symmetryPPT📢All PPTs : https://youtube. They are anisotropic in nature. It would then be possible to draw a Use this fun and interactive Introduction to Symmetry PowerPoint to introduce First Level Learners to the wonderful world of symmetry. Geometry in Nature Denise Hyatt, Angela Long, Jocelyn Johnson, and Nakeesha Trammell. The Fibonacci sequence appears often in nature, with ratios Examples of objects that exhibit line symmetry include many creatures, plants, human faces, bodies, letters of the alphabet, and artworks which can be folded along a Interest in the optics of artificial heterogeneous media rekindled in the last decade. Grade R Symmetry PowerPoint. This is a lovely pack with high quality images and a great PPT slideshow. Christmas Symmetry Worksheet . Geometry in Nature. Reflective Symmetry • Point symmetry - any Symmetry • Definition-The preservation of form and configuration across a point, line or a plane. 45 reviews . May 9, 2009 • Download as PPT, PDF • 5 likes • 28,462 views. 4% of our customers would recommend us to a friend. Keeping children engaged can be a This brilliant resource will help your learners to find out all about symmetry. It is observed from mathematical, Kagome lattice hosts a plethora of quantum states arising from the interplay of topology, spin-orbit coupling, and electron correlations. Types of Patterns 1. Line Symmetry If a shape can be folded in half so that one – A free PowerPoint PPT presentation (displayed as an HTML5 Nature - An algorithm based on symmetry indicators is used to search a crystallographic database and finds thousands of candidate topological materials, The paper presents design of collars of ladies' dresses with use of different types of symmetry, which are inspired by symmetry in nature. Emmy Noether 1918: Symmetry in nature. It also Geometry in Nature. Symmetry, in geometry is a correspondence or matching of 5. The collars are chosen as a special case of fashion design. So why This is known as the rotational symmetry. pdf), Text File (. js, . The document discusses symmetry and lines of symmetry. Fully animated and complete with specially-designed diagrams and illustrations, it's the perfect Bilateral or reflection symmetry is the simplest kind of symmetry. Animal gaits display symmetry in space, time, and permutational symmetries of the legs. Mathematics is found throughout nature. Many natural phenomena exhibit patterns like Geometry, Nature and Architecture - Download as a PDF or view online for free. This document discusses different types of patterns found in nature and their definitions. This handy pack includes a PowerPoint presentation about symmetry with a particular focus on how symmetrical designs are used in Islamic architecture and design. Keeping Nature - A ladder-like arrangement of an ultracold gas of lithium atoms trapped in an optical lattice enables the observation of a symmetry-protected topological phase. It defines symmetry as identical matching of two or more parts of a figure after folding or Patterns like symmetry, spirals, spots and stripes can be found throughout nature and described mathematically. css, and . You can use this resource to combine your class' learning about the natural world with Floquet PT-symmetry, which may be realized by periodically flipping the effective gain/loss distribution in time, Nature 548, 192 (2017). These patterns recur in different contexts and can sometimes be modelled mathematically . Full syllabus notes, lecture and questions for Symmetry Class 7 PPT - Class 7 - Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Symmetry is also used in nature, such as the symmetry of flowers and butterfly wings. In other words, symmetry As indicated by direct band-structure measurements and calculations, tiny native imperfections in bilayer graphene are sufficient to cause the generation of coexisting massive and massless Dirac One 30 Page Symmetry Image Pack – A collection of thirty high quality images that show examples of symmetry in nature, design and architecture. The Fibonacci sequence, where 7. SYMMETRY IN NATURE GRADE: 3-5 TIME: Five 60-minute sessions Frank Lloyd Wright was known for creating art glass designs that incorporated simple shapes, lines, and patterns that appear in the natural world. It discusses rotational symmetry in regular polygons and defines other types of symmetry like Nature’s Geometry: Symmetry and polygons in Nature. The document discusses patterns in nature and Nature - Observations of the decay of 73Sr, when compared to its mirror nucleus 73Br, indicate that the spin assignment of their ground states differ, demonstrating mirror-symmetry violation. Introduction Discovering the link between geometry and nature is not a difficult – A free PowerPoint PPT presentation (displayed as an HTML5 slide show) on PowerShow. By Rebecca Dow, Sara Howard, Julie Russell, Jessie Captivate your students with rich, full color photographs that show the variety of symmetry in nature. With clear explanations and real-life examples in nature, this presentation brings symmetry to life, making Symmetry is present in many areas of everyday life such as art, architecture, textiles, car manufacturing, and rangoli. The document discusses different types of symmetry and shapes found in nature. Adapted from ref. Mathematics can be seen Symmetry and Patterns in Monuments - Free download as Powerpoint Presentation (. Snowflakes are other model of radial symmetry – figure Introduction Symmetry is present in nature and in human culture. Natural patterns include symmetries , trees , spirals , The concept of non-Hermitian parity-time reversal symmetry in optics has given rise to a vast amount of research aimed at exploring some of the exotic features displayed by photonics systems. Some figures, like this tree, Others – A free PowerPoint PPT presentation (displayed as an HTML5 slide Symmetry Symmetry is everywhere you look in Nature Symmetry is when a figure has two sides that are mirror images of one another. It defines symmetry as when a Finding Symmetry in Nature with Kids Lucy thought this flower might be a good example of rotational symmetry. This Review discusses recent developments in the area of non-Hermitian physics, and more specifically the special case of non-Hermitian optical systems with parity–time symmetry. This document discusses different patterns found in nature, including symmetry, MATH IN NATURE: SYMMETRY AND SPIDER WEBS. Aligned with the Australian Curriculum AC9M5SP03 - describe and Symmetry in Nature Worksheet. Draw The Other Half Symmetry Worksheet . Trusted by teachers 98. 4. Unlimited. Look in the mirror at your own face to observe your very own bilateral symmetrical facial features. So why not have a symmetry lesson outside, in nature. pptx), PDF File (. It explains regularities, irregularities, and complexities in the world by organizing patterns and simplifying things. They exhibit directional properties. txt) or read online for free. Definition-The preservation of form and Patterns in Nature - Download as a PDF • Download as PPT, PDF Plants, flowers and fruits have all kinds of patterns, from petal numbers that are in the Fibonacci This handy pack includes a PowerPoint presentation about symmetry with a particular focus on how symmetrical designs are used in Islamic architecture and design. It provides examples of line symmetry seen in This document discusses how patterns and numbers are found throughout nature and the world. Mathematics in Nature - Free download as Powerpoint Presentation (. Leonardo da Vinci’s Vitruvian Man shows Symmetry in Nature PowerPoint. It is observed from mathematical, The beauty of a flower, the majestic tree, even the rock formation exhibits nature’s sense of symmetry. This document discusses different patterns found in nature. Examples of Topological materials discovery has evolved at a rapid pace over the past 15 years following the identification of the first nonmagnetic topological insulators (TIs), topological crystalline Patterns-and-regularities. These have shape and color symmetry. Would highly Patterns in nature are visible regularities of form found in the natural world. This fall leaf is a good example of reflection Symmetry Line Symmetry Shape has line symmetry when one half of it is the mirror image of the other half. Rotation Differentiated Worksheets. 12 reviews . Symmetry can be seen in art, nature, mathematics and other Symmetry Around Us - Download as a PDF or view online for free Maths in Nature: Snowflake Symmetry (Ages 5 - 7) EYFS Symmetrical Patterns Chilli Challenge Cards: Nature Symmetry Flower Symmetry Drawing Activity Pack In addition, there are projects, activities and videos found at the MathArt Virtual Library under the MathArt II menu bar, with symmetry found in the drop down menu. Symmetry is everywhere you look in Nature Symmetry is when a figure has two sides that are mirror images of one another. Fully animated and complete with specially-designed diagrams and illustrations, it's the perfect Geometry in Nature. 10 reviews . Ch 4 Lecture 1 Symmetry and Point Groups • Introduction • Symmetry is present in nature and in human culture. SYMMETRY. Can symmetry help us solve mathematical problems? Maths in nature - Download as a PDF or view online for free. Symmetry is nature’s artwork that creates harmony and balance. It would then be possible to draw a Video Description: Symmetry in Nature for CTET & State TET 2024 is part of Mathematics & Pedagogy Paper 2 for CTET & TET Exams preparation. Flowers often exhibit vertical axes of symmetry, with their petals arranged identically on both sides Symmetry in Nature - Free download as Powerpoint Presentation (. MATH IN NATURE: HONEYCOMBS AND HEXAGONS. Skip to main content Thank Femtosecond optical pulses are used to generate coherent phonons that break inversion symmetry and drive anisotropic terahertz photocurrents in the topological material ZrTe5. 45 reviews Explore more than 67 "Symmetry Powerpoint" resources for teachers, parents and pupils as well as related resources on "Symmetry" Get The basic classification includes Levels of organization, Symmetry, Diploblastic and Triploblastic Organisation, Coelom, Segmentation, and Notochord. Teach Year 3 children about symmetry with this fantastic lesson pack. MATH IN NATURE: FIBONACCI SEQUENCE AND SUNFLOWERS. In this lesson, students will The Symmetry in Nature PowerPoint is a fantastic tool for helping students discover symmetry in the natural world while developing their mathematical understanding. The bundle includes both grid and non-grid sheets for students to challenge themselves appropriately. Fully animated and complete with specially-designed diagrams and illustrations, it's the perfect Geometry in Nature PROJECT 1 - Free download as Powerpoint Presentation (. TRANSFORMATIONS ON A PLANE There are four kinds of transformations in a plane. Email Me This Resource Measurement Location and What is symmetry ? Symmetry is when a shape looks identical to its original shape after being flipped or turned. These media have many unique properties that are absent in homogeneous natural materials, including artificial magnetism at optical frequencies [1–4], negative refraction [5, 6], and strong spatial dispersion [7, 8]. 20, Macmillan Publishers Ltd (c). Something is symmetrical when it is the same on both sides. pptx - Free download as Powerpoint Presentation (. Next, make the connection of symmetry in nature to 10 Fun Ways to Help Preschoolers Develop Early Math Skills - As a parent, you play a key role in building your preschooler’s math skills to set them up for math success in elementary school and beyond. It is an important aspect in the study of Geometry, as an integral component connecting Mathematics to the real world . This document discusses patterns found in nature. Early philosophers studied natural patterns like symmetries, spirals, and waves. Eighth Grade Rotational Symmetry PowerPoint & Google Slides . 2D Shapes PowerPoint. Definition-The preservation of form and This document discusses different types of symmetry found in nature, architecture, art, religious symbols, and music. Line of Symmetry Worksheet. It begins This document discusses the concept of symmetry and lines of symmetry. Symmetry is an important concept in science that is commonly observed in nature. 15 reviews. Flowers offer a variety of Use this fun and interactive Introduction to Symmetry PowerPoint to introduce First Level Learners to the wonderful world of symmetry. Spring and fall are the best seasons for this activity. The human body Mathematics-in-Nature - Free download as Powerpoint Presentation (. To summarize some of the important aspects of non-Hermitian physics and PT symmetry in this review article, we primarily focus on the interplay between conservative and non-conservative processes in photonics. Symmetry refers to an object being unchanged after a transformation, such as reflection. However, anatomical symmetry is broken in some organ systems. Symmetry Can Be Found All Around Us. It covers symmetry patterns like bilateral, mirror, radial and rotational symmetry. Using Symmetry in Chemistry Understand what orbitals are used in bonding Predict IR spectra or Interpret UV Symmetry meaning in maths. Radial symmetry is rotational symmetry 2. com/playlist?list=PLPsnBV8O_4 Symmetry In Math - Download as a PDF • Download as PPT, PDF and glide reflective symmetry. 2 "The laws of nature are but the mathematical thoughts of God" - Euclid Maths in Nature Patterns in nature are visible regularities of form found in the natural world. It begins by defining what a pattern is and explains that patterns can be found SYMMETRY IN NATURE The beautiful dragonfly, presented in figure 1, is an excellent example for bilateral symmetry. Hence, all these categories must be kept in mind while classifying Looking for a great symmetry PowerPoint to use in your next maths lesson? You’re in the right place! This wonderful symmetry PowerPoint resource is great for any maths lesson focusing on shapes and their properties. B. There are three main types of symmetry: line This handy pack includes a PowerPoint presentation about symmetry with a particular focus on how symmetrical designs are used in Islamic architecture and design. Fully animated and complete with specially-designed diagrams and illustrations, it's the perfect Patterns and Numbers in Nature and the World Fibonacci Sequence - Free download as Powerpoint Presentation (. They will explore where tessellation is found in nature and what artist has Does this star have point symmetry? In nature, we can find many examples of symmetry: in flowers and leaves, in our own bodies, and in snowflakes. It's found in art, biology, architecture and all over the natural world. 2 SYMMETRY Symmetry is when an object has two or more equal sides when split in half or in smaller pieces. 19, APS (b); and ref. This sand dollar is slightly less than 3" in Lesson-1-Mathematics-in-Nature. This Use this beautifully illustrated PowerPoint to integrate geometry with an art lesson. Symmetry, orderly, mutually corresponding arrangement of various parts of a body, producing a proportionate, balanced form. The Taj Mahal in Agra, India is one of the most beautiful and Patterns in nature are visible regularities that recur in different contexts and can be mathematically modeled. Even though the Hermiticity of quantum observables was never in doubt, such concepts have motivated discussions on several 2. But math doesn’t need to be tedious for little learners. 1 review . This fossil shows the 5 point "flower" symmetry common to the animal in the Echinodermata phylum. Skip MMW-Lecture1-Patterns and Numbers in Nature - Free download as Powerpoint Presentation (. There are introductory worksheets with simple shapes and information about finding the line, or lines, of symmetry. Using Symmetry in Chemistry • Understand what The document provides instructions for creating a radial symmetry mandala art project. These patterns recur in different contexts and are modelled mathematically. 1) There are three main types of symmetry: reflection, rotation, and translation. Symmetry is seen throughout nature, from the patterns in flowers and trees to the shapes of rocks. I thought it would be cool to share th Instantly access Twinkl's printable and digital K-12 teaching resources, including worksheets, eBooks, games, PowerPoints, Google Slides, and more! Fractals in Nature Natural objects exhibit scaling symmetry, but only over a limited range of scales. This resource is engaging and visually appealing, designed to capture students' attention and spark curiosity. For example, a butterfly has symmetry. html) in your browser cache. Symmetry in Nature PowerPoint. The symmetry of molecules and solids is a very powerful tool for:- • determination and description of structures of molecules. These new properties, related to the resonance nature of the Use this fun and interactive Introduction to Symmetry PowerPoint to introduce First Level Learners to the wonderful world of symmetry. Draw The Other Half Symmetry Worksheet. They also tend to be “roughly” self- similar, appearing more or less the same Symmetry is all around us. Chirality of an organic compound The most common, cause of chirality in an organic molecule is the presence of a tetrahedral carbon atom bonded to four different Symmetry is seen throughout nature, from the patterns in flowers and trees to the shapes of rocks. 396 views • 17 slides.  Ther are also two different worksheets which are differentiated Full syllabus notes, lecture and questions for PPT: Symmetry - Mathematics for Grade 6 - Grade 6 In nature, many organisms exhibit symmetry, such as butterflies and flowers. The various activity worksheets feature examples of symmetry in nature. Different Types of Symmetry • Reflection Symmetry • Divides figure in halves that are mirror images • Hearts, Squares, Diamonds • Rotation Symmetry • When object is turned 6 Symmetry in Nature Examples of symmetry abound in nature. Symmetry. You can use this resource to combine your class' learning about the natural world with learning about symmetry. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, arrays, cracks and stripes. Preschoolers can develop essential early math skills through fun, engaging everyday activities. There is a form of bilateral symmetry, like the reflection of an image in a lake that can be divided into two identical parts; and it can also be radial when the image forms around a central point and "radiates" to all sides, such as an open flower or a yellow dandelion. Lines of Symmetry Differentiated Activity Worksheet for 3rd-5th Grade. Symmetry is seen in structures like starfish and flowers, while spirals in shells, pinecones and sunflowers relate to the Fibonacci sequence. 2D Shape Hunt Colouring Activity This PowerPoint is a great way to support your teaching of rotational symmetry. You can check for symmetry in a shape by drawing a mirror line down the middle and seeing if both halves are identical. It explains that mathematics is the key to understanding the physical Geometry in Nature By Rebecca Dow, Sara Howard, Julie Russell, Jessie Buchheim, and Jordann Tomasek Symmetry Definition-The preservation of form and configuration – A free PowerPoint PPT presentation (displayed as MATHEMATICAL PATTERNS IN NATURE Mathematics is seen in many beautiful patterns in nature, such as in symmetry and spirals. The Symmetry in Nature PowerPoint is a fantastic tool for helping students discover symmetry in the natural world while developing their mathematical understanding. 7 reviews Symmetry in Nature PowerPoint.  Ther are also two different worksheets which are differentiated Symmetry surrounds us. Dragonflies and Butterflies. In order to read the online edition of The Feynman Lectures on Physics, javascript must be supported by your browser and enabled. Download. Here, we report symmetry-breaking electronic orders Nature Communications - Quantum critical points in metallic ferromagnets are rare and their mechanism is poorly understood. Reflective Symmetry • Also known as flips, one half of an image is the mirror image Symmetry is found throughout nature, architecture, and art. Second Grade An MMW - PPT1 Pattterns and Numbers - Free download as Powerpoint Presentation (. 8 reviews . This document discusses the presence of mathematics in nature. Symmetry PowerPoint. The notes and questions for Symmetry in Nature have been prepared according to the Symmetry in Nature PowerPoint. SYMMETRY – a sense of harmonious and beautiful proportion of balance or an object is Symmetry PowerPoint - Free download as Powerpoint Presentation (. txt) or view presentation slides online. Gamache showcases the concept of symmetry, highlighting its presence in nature, animals, human faces, art, and Project the slides on the screen and start the instruction with a discussion and drawing activity to introduce the concept of symmetry in nature and the world around us. Investigating Lines of Symmetry Worksheet. 1 Patterns and Numbers in Nature and the World - Free download as Powerpoint Presentation (. Downloads. With clear explanations and a quiz to consolidate learning. Lines of Symmetry Display Poster . Content: Symmetry is when an object looks the Symmetry PowerPoint - Download as a PDF or view online for free Submit Search. Winter Themed Symmetry Worksheets . . ppt), PDF File (. We can see symmetry in nature: Symmetry is used in architecture: Use this fun and interactive Introduction to Symmetry PowerPoint to introduce First Level Learners to the wonderful world of symmetry. This document provides an outline for a course on mathematics SYMMETRY Symmetry is everywhere you look in nature. Nature loves symmetry Most objects found in nature have This PowerPoint presentation created by Mrs. Jellyfish have D4 symmetry - four rotations of 90 degrees each. With clear explanations and real-life examples in nature, this presentation brings symmetry to life, making It then provides examples of shapes with lines of symmetry like hearts and flags. Your children will have to identify points of symmetry, plus there are interactive elements too. 1) Reflection 2) Translation 3) Rotation 4) Dilation REFLECTION Here is another example of a reflection: Symmetry Grade Level: 4-6 Teacher Guidelines pages 1 – 2 Instructional Pages pages 3 – 4 Activity Page pages 5 - 8 Practice Page page 9 Homework Page page 10 Answer Key page 11 - 12 are Hamiltonians respecting parity–time (PT) symmetry2–7. Challenge them to find the lines of symmetry in snowflakes, peacocks, flowers, owls, zebras Symmetry in Nature Symmetry is fun to learn about because it is all around us in nature. Hover to zoom. It can be described through symmetry operations such as rotations, reflections, and Nature of Mathematics - Free download as Powerpoint Presentation (. People, animals, plants, everything on the earth and outside is symmetrical. 3. The principle of symmetry is of This lovely PowerPoint on symmetry is a wonderful way to introduce your students to symmetry. Bilateral symmetry in organisms has been shown to be controlled genetically. Rotational symmetry is explained using examples like snowflakes and planets Reflective Symmetry • Also known as line symmetry, means that one half of an image is the mirror image of the other half. It would then be possible to draw a line Nature’s Geometry: Symmetry and polygons in Nature Symmetry Can Be Found All Around Us. If you drew a line down the middle of the butterfly, both sides would be the same. A Dragonflys Life An Adult Dragonfly: Has 2 sets of wings. Keeping children engaged Symmetry Drawing Bundle is a collection of nature inspired symmetry drawing templates. Children will learn to identify line symmetry in 2D shapes as well as explore reflection symmetry. Symmetry drawing is great for students who finish classwork early, foundation art and drawing skills, and a fun way to end the week. Mathematics can be used to model and explain patterns found 3 Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered Shapes-Many geometric shapes are found in nature-Repeating patterns- some are the same size Download ppt "Geometry in Nature. Definition-The preservation of Dive into the world of geometric balance with our Second Grade An Introduction to Symmetry PowerPoint & Google Slides Presentation, an engaging and educational resource crafted to illuminate the concept of lines of symmetry in This document presents a maths project on symmetry by Riya Ben of class 7.