How Facebook Has Destroyed Privacy Boundaries Essay

How Facebook Has Destroyed Privacy Boundaries - Essay Example The website has come under the limelight time and again. Previously it was in the limelight as a business model for innovation and hallmark breakthroughs but in recent times it has been scrutinized for breaches of privacy. The various forms of breach of privacy have been recognized and investigated and are confirmed phenomenon leaving little to doubt them anymore (Iachello and Hong). Some breaches of privacy are caused due to users overlooking fine print details while other breaches of privacy occur due to online surveillance. In addition to everything else, certain forms of breach of privacy occur due to the inherent design of social networking platforms. This paper will focus on the various forms of breach of privacy that have resulted from the use of Facebook whether these breaches were intentional or otherwise. Furthermore, the consequences of these breaches will be looked into in detail to gauge their effects on ordinary people. Another major factor that limits the amount of inf ormation carried by human beings is the limit on information delivered at any one point in time through conversations. It would be unrealistic to assume that a person could convey all kinds of personal and family information to another in one meeting alone. However, this situation is totally reversed when using computing platforms to interact. People who use social networking websites such as Facebook will realize that a large amount of information has to be divulged in order to sign up for such services.  

Usefulness Of Maxima And Minima Of Functions Engineering Essay

Usefulness Of Maxima And Minima Of Functions Engineering Essay The mathematical concept of a function expresses the intuitive idea that one quantity(input) completely determines another quantity (output). A function assigns a unique value or output to each input of a specified type. The argument and the value may be real numbers, but they can also be elements from any given sets: the domain and the co-domain of the function. Whenever a relationship exists between two variables (or quantities) such that for every value of the first, there is only one corresponding value of the second, then we say:The second variable is a function of the first variable. The first variable is the independent variable (usually x), and the second variable is the dependent variable (usually y). The independent variable and the dependent variable are real numbers. The term function is just a type of operator which transforms the given input to output according to the given conditions. This operator relates two or more quantities to each other, the quantities are known as variables. Out of total variables only one is independent and all other are dependent on that variable. One precise definition of a function is that it consists of an ordered triple of sets, which may be written as (X, Y, F). X is the domain of the function, Y is the co-domain, and F is a set of ordered pairs. In each of these ordered pairs (a, b), the first element a is from the domain, the second element b is from the co-domain, and every element in the domain is the first element in one and only one ordered pair. The set of all b is known as the image of the function. Some authors use the term range to mean the image, others to mean the co-domain. The notation Æ’:Xà ¢Ã¢â‚¬  Ã¢â‚¬â„¢Y indicates that Æ’ is a function with domain X and co-domain Y. (Domain implies input whereas range or co-domain implies output.) In most practical situations, the domain and co-domain are understood from context, and only the relationship between the input and output is given. Thus is usually written as Here the two variables are x and y out of which x is independent and y is dependent on x. From the other side if we consider y as independent variable then x is dependent on y. Every function can be plotted on graph or more precisely Argand Plain. The graph of function may be a straight line, a continuous curve, a circle, an ellipse or even a point also. HISTORY OF MAXIMA AND MINIMA: Since origin of life, all people knew, talked, applied the concept of maxima and minima in their daily lives without even knowing about the concept of maxima and minima. In the earlier phase of time the kings used to estimate the maximum and minimum army of the opposite side, doctors used to record minimum and maximum symptom of any disease, cooks used to estimate the maximum and minimum quantity of food or people before any function, the businessmen used to estimate maximum and minimum profit or loss in any transaction. Even today also the women in the house prepare the food according to maximum or minimum consumption by each individual. Sir Issac Newton, a great scientist, invented the concept of functions and hence concept of maxima or minima. Since then his concepts are very usefully applicable in our daily lives. PRESENT TIME CONCEPTS OF MAXIMA AND MINIMA: The terms maxima and minima refer to extreme values of a function, that is, the maximum and minimum values that the function attains. Maximum means upper bound or largest possible quantity. The absolute maximum of a function is the largest number contained in the range of the function. That is, if f(a) is greater than or equal to f(x), for all x in the domain of the function, then f(a) is the absolute maximum. For example, the function f(x) = -162 + 32x + 6 has a maximum value of 22 occurring at x = 1. Every value of x produces a value of the function that is less than or equal to 22, hence, 22 is an absolute maximum. In terms of its graph, the absolute maximum of a function is the value of the function that corresponds to the highest point on the graph. Conversely, minimum means lower bound or least possible quantity. The absolute minimum of a function is the smallest number in its range and corresponds to the value of the function at the lowest point of its graph. If f(a) is less t han or equal to f(x), for all x in the domain of the function, then f(a) is an absolute minimum. As an example, f(x) = 322 32x 6 has an absolute minimum of -22, because every value of x produces a value greater than or equal to -22. In some cases, a function will have no absolute maximum or minimum. For instance the function f(x) = 1/x has no absolute maximum value, nor does f(x) = -1/x have an absolute minimum. In still other cases, functions may have relative (or local) maxima and minima. Relative means relative to local or nearby values of the function. The terms relative maxima and relative minima refer to the largest, or least, value that a function takes on over some small portion or interval of its domain. Thus, if f(b) is greater than or equal to f(b  ± h) for small values of h, then f(b) is a local maximum; if f(b) is less than or equal to f(b  ± h), then f(b) is a relative minimum. Finding the maxima and minima, both absolute and relative, of various functions represents an important class of problems solvable by use of differential calculus. The theory behind finding maximum and minimum values of a function is based on the fact that the derivative of a function is equal to the slope of the tangent. When the values of a function increase as the value of the independent variable increases, the lines that are tangent to the graph of the function have positive slope, and the function is said to be increasing. Conversely, when the values of the function decrease with increasing values of the independent variable, the tangent lines have negative slope, and the function is said to be decreasing. Precisely at the point where the function changes from increasing to decreasing or from decreasing to increasing, the tangent line is horizontal (has slope 0), and the derivative is zero (With reference to figure 1, the function is decreasing to the left of point A, as well a s between points B and C, and increasing between points A and B and to the right of point C). In order to find maximum and minimum points, first find the values of the independent variable for which the derivative of the function is zero, then substitute them in the original function to obtain the corresponding maximum or minimum values of the function. Second, inspect the behavior of the derivative to the left and right of each point. A wide variety of problems can be solved by finding maximum or minimum values of functions. For example, suppose it is desired to maximize the area of a rectangle inscribed in a semicircle. The area of the rectangle is given by A = 2xy. The semicircle is given by x2 + y2 = r2, for y à ¢Ã¢â‚¬ °Ã‚ ¥ 0, where r is the radius. To simplify the mathematics, note that A and A2 are both maximum for the same values of x and y, which occurs when the corner of the rectangle intersects the semicircle, that is, when y2 = r2 x2. Thus, we must find a maximum value of the function A2 = 42(r2 -x2) = 4r2x2 44. The required condition is that the derivative be equal to zero, that is, d(A2)/dx = 8r2x 163 = 0. This occurs when x = 0 or when x = 1à ¢Ã‚ Ã¢â‚¬Å¾2(r à ¢Ã‹â€ Ã… ¡ +2 ). Clearly the area is a maximum when x = 1à ¢Ã‚ Ã¢â‚¬Å¾2(r à ¢Ã‹â€ Ã… ¡ +2 ). Substitution of this value into the equation of the semicircle gives y = 1à ¢Ã‚ Ã¢â‚¬Å¾2(r à ¢Ã‹â€ Ã… ¡ +2 ), that is, y = x. Thus, the max imum area of a rectangle inscribed in a semicircle is A = 2xy = r2. The problem of determining the maximum or minimum of function is encountered in geometry, mechanics, physics, and other fields, and was one of the motivating factors in the development of the calculus in the seventeenth century. Let us recall the procedure for the case of a function of one variable y=f(x). First, we determine points where f'(x)=0. These points are called critical points. At critical points the tangent line is horizontal. This is shown in the figure below. . The second derivative test is employed to determine if a critical point is a relative maximum or a relative minimum. If f()>0, then x is a relative minimum. If f() The notions of critical points and the second derivative test carry over to functions of two variables. Let z=f(x, y). Critical points are points in the xy-plane where the tangent plane is horizontal. Since the normal vector of the tangent plane at (x,y) is given by The tangent plane is horizontal if its normal vector points in the z direction. Hence, critical points are solutions of the equations: because horizontal planes have normal vector parallel to z-axis. The two equations above must be solved simultaneously. The Second Derivative Test for Functions of Two Variables How can we determine if the critical points found above are relative maxima or minima? We apply a second derivative test for functions of two variables. Let (x,y) be a critical point and define We have the following cases: If D>0 and (,).) If D>0 and (,).)>0, then f(x,y) has a relative minimum at ( ,).). If D If D=0, the second derivative test is inconclusive. Maxima and Minima in a Bounded Region Suppose that our goal is to find the global maximum and minimum of our model function above in the square -2 Relative extrema in the interior of the square. Relative extrema on the boundary of the square. Corner Points. We have already done step 1. There are extrema at (1, 0) and (-1, 0). The boundary of square consists of 4 parts. Side 1 is y=-2 and -2 The original function of 2 variables is now a function of x only. We set g'(x)=0 to determine relative extrema on Side 1. It can be shown that x=1 and x=-1 are the relative extrema. Since y=-2, the relative extrema on Side 1 are at (1,-2) and (-1,-2). On Side 2 (x=-2 and -2 We set h'(y)=0 to determine the relative extrema. It can be shown that y=0 is the only critical point, corresponding to (-2,0). We play the same game to determine the relative extrema on the other 2 sides. It can be shown that they are (2,0), (1,2), and (-1,2). Finally, we must include the 4 corners (-2,-2), (-2,2), (2,-2), and (2,2). In summary, the candidates for global maximum and minimum are (-1,0), (1,0), (1,-2), (-1,-2), (-2,0), (2,0), (1,2), (-1,2), (-2,-2), (-2,2), (2,-2), and (2,2). We evaluate f(x,y) at each of these points to determine the global max and min in the square. The global maximum occurs (-2,0) and (1,0). This can be seen in the figure above. The global minimum occurs at 4 points: (-1,2), (-1,-2), (2,2), and (2,-2). One of the great powers of calculus is in the determination of the maximum or minimum value of a function. Take f(x) to be a function of x. Then the value of x for which the derivative of f(x) with respect to x is equal to zero corresponds to a maximum, a minimum or an inflexion point of the function f(x). The derivative of a function can be geometrically interpreted as the slope of the curve of the mathematical function y(t) plotted as a function of t. The derivative is positive when a function is increasing toward a maximum, zero (horizontal) at the maximum, and negative just after the maximum. The second derivative is the rate of change of the derivative, and it is negative for the process described above since the first derivative (slope) is always getting smaller. The second derivative is always negative for a hump in the function, corresponding to a maximum. A critical point (x,y) of f is a point where both the partial derivatives of the functions vanish. A local maximum, or a local minimum, is a critical point. In one variable, local maxima and minima are the only `nondegenerate critical points. In two or more variables, other possibilities appear. For instance one has the saddle point, like the critical point of at (0; 0). In some directions this looks like a maximum, in other directions this looks like a minimum. We try to classify critical points by looking at the second derivatives. APPLICATIONS OF MAXIMA AND MINIMA IN DAILY LIFE: There are numerous practical applications in which it is desired to find the maximum or minimum value of a particular quantity. Such applications exist in economics, business, and engineering. Many can be solved using the methods of differential calculus described above. For example, in any manufacturing business it is usually possible to express profit as a function of the number of units sold. Finding a maximum for this function represents a straightforward way of maximizing profits. In other cases, the shape of a container may be determined by minimizing the amount of material required to manufacture it. The design of piping systems is often based on minimizing pressure drop which in turn minimizes required pump sizes and reduces cost. The shapes of steel beams are based on maximizing strength. Finding maxima or minima also has important applications in linear algebra and game theory. For example, linear programming consists of maximizing (or minimizing) a particular quantity while requiring that certain constraints be imposed on other quantities. The quantity to be maximized (or minimized), as well as each of the constraints, is represented by an equation or inequality. The resulting system of equations or inequalities, usually linear, often contains hundreds or thousands of variables. The idea is to find the maximum value of a particular variable that represents a solution to the whole system. A practical example might be minimizing the cost of producing an automobile given certain known constraints on the cost of each part, and the time spent by each laborer, all of which may be interdependent. Regardless of the application, though, the key step in any maxima or minima problem is expressing the problem in mathematical terms. Everything in this world is based on the concept of maxima and minima, every time we always calculate the maximum and minimum of every data. Now-a-days results are also based on the concepts of grades which is again based on the concept of maxima and minima.

open fracture of the radius :: essays research papers

Injury report: Open fracture of the Radius. A triathlon involves swimming, running and then biking a set track. A triathlete fell from his bike during training, due to the wet road. He landed awkwardly on his bike. His Radius was broken because he landed with his arm on the handle bars of the bike. The force at which he landed on the handle bars caused his Radius to break and pierce the skin. A cracked bone is called a fracture. Fractures are most likely to occur in the limb bones. (Radius and Ulna; Tibia and Fibula) Fractures are named according to the certain features which separate the different types of fracture. †¢Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Closed fracture. The bone is broken but the overlying skin surface is not damaged. †¢Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Open fracture. The broken ends of the bone have pierced the surface of the skin. †¢Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Compound fracture. The fractured bone has caused other injuries, e.g. the rib may have penetrated the lung. The triathlete has an open fracture of the Radius. (Image 1) As can be seen in the above picture the Radius is a bone in the lower arm, on the same side of the arm as the thumb. As people when falling-outstretch their arms to break their fall-the radius may received several quite heavy blows. This may weaken the joints around the radius and may cause it to dislocate. The triathlete has landed on the side of his radius, and the radius has broken in half and has pierced the skin. This leaves the body vulnerable to infection and obviously isn’t pleasant for the triathlete. Below is an image of the femur and on it is labeled the different types of bone and where they may be found. The white hard bone on the outside is called the compact bone. On the inside of the shaft is the bone marrow. Inside the epipysis is the spongy bone. Surrounding the ends of the bone is cartilage which eases movement between bones. Osteo=Bone. The bone marrow produces red and white blood cells.   Ã‚  Ã‚  Ã‚  Ã‚  Chondrin=Cartilage.   Ã‚  Ã‚  Ã‚  Ã‚  (Image 2)   Ã‚  Ã‚  Ã‚  Ã‚   Above is a diagram of the structure of a mature bone. It shows what each different part of the bone looks like under a microscope, and where those parts of bone are found. The top of this bone is called the head ( this also applies to the radius) The long, thin part of the bone that gives the bone its length is called the shaft Immediate first aid†¦ When bones are broken (The following must be done in a way that would prevent further injury) the immediate first aid is to†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.

Non Biodegradable

Non-biodegradable waste made up roughly one-third of the municipal solid waste produced in the U. S. in 2009 (see References 1, page 6). The U. S. Environmental Protection Agency recommends recycling whenever possible, and disposing of your trash at a combustion facility or in a landfill only when recycling is not possible (see References 1, page 11). Hazardous waste should be handled separately by your local sanitation department or by private companies that specialize in safe disposal of toxins (see References 2).Recycling Separate glass, plastic and metal from other non-biodegradable waste for recycling. Many urban and suburban areas have curbside recycling programs; if such a program is not available, take recyclable materials to the nearest collection facility for processing. Recycling saves space in landfills and reduces the amount of virgin materials that must be mined or manufactured to make new products, saving energy and reducing global climate change in the process. (See R eferences 3) CombustionSome non-biodegradable waste like used rubber tires and plastic can be burned at combustion facilities. Most of these facilities use the heat generated by incineration to make energy in the form of steam or electricity, which reduces their demand for other nonrenewable resources, including coal and petroleum. In 2009, combustion facilities burned 3. 1 million tons of solid waste, mostly used tires. Combustion of municipal waste also reduces the volume of trash that ends up in landfills. (See References 1, page 166) LandfillsLandfills provide long-term storage for non-biodegradable waste. Ideally, landfills are carefully situated to prevent contamination from entering surrounding soil and water, and managed to reduce odor and pests as much as possible. (See References 4) Federal regulations require careful monitoring in and around the site. Hazardous Waste Disposal Some products like motor oil, pesticides, batteries and paint are potentially hazardous to sanita tion workers and the general population as a whole.They are also more dangerous to the environment than inert materials like plastic or rubber. Many communities offer special collection and disposal programs to deal with household hazardous waste as safely as possible. In areas with no such programs, it's legal to dispose of household hazardous waste in the trash. Follow any special disposal instructions listed on the original container. Before doing so, however, contact the manufacturer or retailer of the material you need to dispose of to ask if they accept old materials for reuse or recycling.

International business climate Essay

There are various factors which are used in measuring the business climate of a nation and also globally. Some of these factors are energy costs, business income tax levels, market size, life’s quality, infrastructure, incentives, workforce availability and others. Globally, the investors are known to monitor the share prices of most business corporations in order to make an informed business on the companies or the market to invest in. According to Guy (2009)and Katsioloudes&Hadjidakis, (2007), business climate globally has been quite harsh on the investors. Some of the business rules in most countries are not conducive for the business climate. These are rules that are quite unstable, disloyal and the corruption is completely out of hand. During crisis, investors usually sell the shares that belong to the entire business in order to avoid losses. This hence affects the entire business adversely. According to the literature review that has been conducted on the international business climate, most multinational companies enjoy relationships and hence have merged in order to ensure competition. Most countries have a vast set of regulations and laws that do affect business operations. As Kirpalani (p. 114) asserts a country like the UK has very active monopoly policies. The monopoly commission plays a very vital role as far as mergers and takeovers are concerned. The UK law does permit the mergers commission and monopolies to investigate, block and delay all the proposed mergers that are not of public interest. Social factors also have a major influence on global business climate. Communities on global business climate are very keen on the way the company does utilize their income in order to support local people as far as destination economies are concerned. Their main interest is to see the local people engage in the foreign companies. They do expect all the multinational companies to be involved in some social activities for example helping the poor people. International business climate are also involved in conserving the environment as every business is going green. There are various government policies that do affect business activities. To ensure that there are low levels of pollution, governments should also establish those policies for example emissions standards. The political environment has set various laws and has aimed at reducing the corporate taxes in order to encourage some of the foreign investments in Africa and Asia (Scaffer et al, 2008). Most of the economies in the global international climate have also invested in effective communication facilities to enable business transactions. If we have to involve the issue of Switzerland in the international business climate we acknowledge the fact that just as the international climate has incorporated economic, cultural, legal as well as political issues so has Switzerland. One of the reasons that make Switzerland cope and suit in the international business climate is the fact that its legal climate is quite transparent and has regulations that are not discriminative. It has a legal system that governs the local and international business activities and stops anti- competitive behavior. Its political climate is effective and very stable. If we are to compare the international climate with that of Switzerland, it is patent that Switzerland’s international climate is better. Therefore, with that in mind there ought to be some recommendations for the international business climate. Switzerland happens to be one of the leading countries globally when it comes to the IT infrastructure. Some of the factors that do work in its favor comprise of issues like security, telecoms competition and government support. The official currency of Switzerland has remained to be Swiss Franc (CHF). It is one of the currencies that has always been used in the country and is quite strong as well as stable over many years. It is convertible and is not controlled by the government. It also has one of the best banking sectors in Switzerland and one of the biggest commercial bank. The communication systems in Swiss are vast and quite modern. Its domestic system comprises of an extensive cable as well as a microwave network. It has the best reputation when it comes to transportation as it has the most efficient and extensive public transportation globally. Its economy is the best and all the Swiss citizens are entitled to education. For those who are financially deprived, the government is responsible for paying their meals, transportation, books and other amenities. The citizens are free from other foreign country and are only subject to the laws of their country. Since it is not part of EU and UN, the government is also free from the outside regulations. Its tri level system of politics is effective since the country and state bodies are usually granted high control levels. The collegial system of Federal council contributes highly to its political stability. Switzerland economy is so effective and has mounted to be the global leading public and medical health infrastructures. It tops the list of all European countries despite the fact it is not a member of EU. As compared to the international business climate, culturally, there main priority has been protection of the environment. Their regulation standards are quite high and efficient making the industry grow at high rates. It is one of the vast and major exporters of both goods and services and a big supplier within Europe after Japan and USA. The climate of Switzerland is definitely what can be termed as pro business. Just like the international climate, it has also adopted a legislative act that promotes economic attractiveness for all businesses. It has created a wonderful appealing economy for business. They also have an advantage of a having high standards of production. Switzerland was ranked by the World Economic Global Competitiveness Report as the global’s most competitive economy (Ina, 2010). It has a sound environment, infrastructure, efficient market and a high technological innovation. The major laws that govern the foreign investment are the Swiss Code of obligations, Securities Law, Cartel Law and Lex Friedrich. Recommendations for International Business climate The international business climate is yet to be what can be termed as perfect. It is therefore the duty of each nation to make sure that everything is running smoothly. In most third world countries, the investors are always at risk. There ought to be firm laws governing each country and protecting businesses from being affected by inflation. Just like in Switzerland, nations need to improve on their efficiency, security and laws in order to have an appealing business climate. The political climate should also be enhanced into one that can accommodate business effectively. It is the duty of the legal system to make sure all social evils are cubed for example corruption in order for businesses to survive. There should be a strong relationship with other foreign countries in order for international trade to survive. Other laws should be introduced whose measures should include tax breaks as well as investment credits for the small companies. There should be strict safety environmental regulations and the government should also offer subsidies and a wonderful climate for businesses. Conclusion Though the international business climate is so much like that of Switzerland, Switzerland has one of the best business climates that are quite appealing. The international business climate should emulate Switzerland and aim to make their climate appealing. This can be done through adoption of laws that protect businesses, unification of all those who are concerned and eradication of all social evils like corruption.

How to Get Out of the Sophomore Slump

How to Get Out of the Sophomore Slump In your sophomore year in college? Feeling uninspired and unmotivated? You just might be in whats known as the college sophomore slump. For most students, its what happens during your second year of college: youre over the excitement of your first year but not close enough to graduating yet to be focusing on life after college. So whats a college student to do in the meantime? Take a Class for Fun You might be feeling slumpish because you are having to take tons of prereqs before you can get into the nice, meaty courses required for your major. Or you may not even be sure what to major in. Either way, add a little spice to your routine by taking a class just for fun. It can be yoga, ballet, an art class, or anything thats out of the ordinary for you. Join a New Club or Organization Your first year in school, you were probably so busy adjusting to life as a college student that your time management skills were shall we say less than stellar. But now that you know the ropes, join a new club or organization that will provide you with a creative outlet and something enjoyable to do each week. Get Involved in Student Government Even if youve never done student government before, see if you can represent your residence hall, your academic class, or even a constituency you belong to (like transfer students, for example). It can be a great way to keep you motivated to talk to other students, stay on top of current issues, and develop some leadership skills. (Not to mention that it looks good on your resume.) Volunteer on Campus No matter where you go to school, chances are that there is some kind of volunteer program you can join. See who needs volunteers this year and you just might end up motivating yourself along with others. Volunteer in the Local Community Maybe a change of scene is more whats needed. If so, see what volunteer options are available in your local community. Mentor First-year Students You just might be in the sophomore slump because you are doing well in college which means that perhaps you can be a good role model for incoming first-year students who need some guidance about adjusting to college life. See if your school has a mentoring program you can join and if not, see about starting one yourself! Get a Fun Job On Campus True, most students work in college for the money. But if you need to mix things up a little, this can be a great way to still get income while also enjoying yourself. Work in the campus coffee shop, at the theater, or in any other avenue that offers a fun, engaging environment. Get a Fun Job Off Campus Perhaps you do need a change of scene from your campus but dont have the time to volunteer. Try to combine both your financial needs and your need for change into an off-campus job that is interesting and something new. Get Involved Politically What are local politics like near your school? Can you volunteer on someones campaign? Join a national campaign for a person or an issue you care about? Become involved in a movement for a cause that is near and dear to your heart? Start Planning a Great Trip Sophomore year can be a little challenging because there often isnt one big thing to look forward to. So why not create your own highlight of the year? See what your options are for planning a fun trip over Thanksgiving break, winter break, spring break, or even a long weekend coming up. It just might do the trick of getting you out of your sophomore slump and back into your normal groove.

Laetoli - 3.5 Million Year Old Hominin Footprints

Laetoli - 3.5 Million Year Old Hominin Footprints Laetoli is the name of an archaeological site in northern Tanzania, where the footprints of three homininsancient human ancestors and most likely Australopithecus afarensiswere preserved in the ash fall of a volcanic eruption some 3.63-3.85 million years ago. They represent the oldest hominin footprints yet discovered on the planet.   The Laetoli footprints were discovered in 1976, eroding out of a gully of the Nagarusi river, by team members from Mary Leakeys expedition to the main Laetoli site. Local Environment Laetoli lies in the eastern branch of the Great Rift Valley of eastern Africa, near the Serengeti Plain and not far from Olduvai Gorge. Three and a half million years ago, the region was a mosaic of different ecotones: montane forests, dry and moist woodlands, wooded and unwooded grasslands, all within about 50 km (31 miles) of the footprints. Most Australopithecine sites are located within such regionsplaces with a wide variety of plants and animals nearby. The ash was wet when the hominins walked through it, and their soft print impressions have given scholars in-depth information about the soft tissue and gait of Australopithecines not available from skeletal material. The hominin prints are not the only footprints preserved in the wet ashfall: animals walking through the wet ash included elephants, giraffes, rhinoceroses and a wide variety of extinct mammals. In all there are 16 sites with footprints in Laetoli, the largest of which has 18,000 footprints, representing 17 different families of animals within an area of about 800 square meters (8100 square feet). Laetoli Footprint Descriptions The Laetoli hominin footprints are arranged in two 27.5 meter (89 foot) long trails, created in moist volcanic ash which later hardened because of desiccation and chemical change. Three hominin individuals are represented, called G1, G2, and G3. Apparently, G1 and G2 walked side by side, and G3 followed along behind, stepping on some but not all of the 31 footprints of G2. Based on known ratios of the length of a bipedal foot versus hip height, G1, represented by 38 footprints, was the shortest individual of the three, estimated at 1.26 meters (4.1 feet) or less in height. Individuals G2 and G3 were largerG3 was estimated at 1.4 m (4.6 ft) tall. G2s steps were too obscured by G3s to estimate his/her height. Of the two tracks, G1s footprints are the best preserved; the track with footprints of both G2/G3 proved difficult to read, since they overlapped. A recent study (Bennett 2016) has allowed scholars to identify G3s steps apart from G2 more clearly, and reassess the hominin heightsG1 at 1.3 m (4.2 ft), G3 at 1.53 m (5 ft). Who Made Them? At least two sets of the footprints have been definitely linked to A. afarensis, because, like the fossils of afarensis, the Laetoli footprints do not indicate an opposable great toe. Further, the only hominin associated with Laetoli area at the time is A. afarensis. Some scholars have ventured to argue that the footprints are from an adult male and female (G2 and G3) and a child (G1); others say they were two males and a female. Three dimensional imaging of the tracks reported in 2016 (Bennett et al.) suggests that G1s foot had a different shape and depth of heel, a different hallux abduction and a different definition of the toes. They suggest three possible reasons; G1 is a different hominin from the other two; G1 walked at a different time from G2 and G3 when the ash was sufficiently different in texture, producing differently shaped impressions; or, the differences are a result of foot size / sexual dimorphism. In other words, G1 may have been, as others have argued, a child or a small woman of the same species. While there is some ongoing debate, most researchers believe that the Laetoli footprints show that our Australopithecine ancestors were fully bipedal, and walked in a modern manner, heel first, then toe. Although a recent study (Raichlen et al. 2008) suggests that the speed at which the footprints were made might affect the kind of gait required to make the marks; a later experimental study also led by Raichlen (2010) provides additional support for bipedalism at Laetoli. The Sadiman Volcano and Laetoli The volcanic tuff in which the footprints were made (called the Footprint Tuff or Tuff 7 at Laetoli) is a 12-15 centimeter (4.7-6 inches) thick layer of ash which fell on this region from the eruption of a nearby volcano. The hominins and a wide variety of other animals survived the eruptiontheir footprints in the muddy ash prove thatbut which volcano erupted has not been determined. Until relatively recently, the source of the volcanic tuff was thought to be the Sadiman volcano. Sadiman, located about 20 km (14.4 mi) southeast of Laetoli, is now dormant, but was active between 4.8 and 3.3 million years ago. A recent examination of outflows from Sadiman (Zaitsev et al 2011) showed that the geology of Sadiman does not fit perfectly with the tuff at Laetoli. In 2015, Zaitsev and colleagues confirmed that it was not Sadiman and suggested that the presence of nephelinite in Tuff 7 points to the nearby Mosonic volcano, but admit that there is not conclusive proof as of yet. Preservation Issues At the time of excavation, the footprints were buried between a few cm to 27 cm (11 in) deep. After excavation, they were reburied to preserve them, but the seeds of an acacia tree was buried within the soil and several acacias grew in the region to heights of over two meters before researchers noticed. Investigation showed that although those acacia roots did disturb some of the footprints, burying the footprints was overall a good strategy and did protect much of the trackway. A new conservation technique was begun in 1994 consisting of application of a herbicide to kill all the trees and brush, the placement of biobarrier mesh to inhibit root growth and then a layer of lava boulders. A monitoring trench was installed to keep an eye on the subsurface integrity. See Agnew and colleagues for additional information on the preservation activities. Sources This glossary entry is a part of the About.com guide to Lower Paleolithic, and the Dictionary of Archaeology. Agnew N, and Demas M. 1998. Preserving the Laetoli foodprints. Scientific American 279(44-55). Barboni D. 2014. Vegetation of Northern Tanzania during the Plio-Pleistocene: A synthesis of the paleobotanical evidences from Laetoli, Olduvai, and Peninj hominin sites. Quaternary International 322–323:264-276. 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