Triangles - Types And Uses

foreign hi everybody what's going on did not transition uh hey I'm skip Alzheimer welcome to the AV Geeks lunchtime streaming show um yeah that was some very warped 16 millimeter film that was curled and it uh it was so cruel that we ran it backwards and then I forgot to fix the uh and make it go forwards but there you go that's uh some New York scenes um and yeah uh so we watch old 16 millimeter films and the first one we're gonna watch is uh triangles types and uses enjoy foreign have you ever cut across a vacant lot we know it is shorter to Walk This Way than it is to walk around the corner one way to find out how much shorter is to count your steps but there is another more accurate way we'll find out about it as we learn about triangles as you probably know a triangle is a closed figure having three sides and three angles we can also Define a triangle this way a figure composed of three points and the line segments connecting them triangles are not only important to us in mathematics but are also commonly used as an important element in architecture and in engineering design we can identify triangles by relationships among their sides in an equilateral triangle the three sides are equal with two equal sides we can form an isosceles triangle a scalene triangle has no two equal sides the perimeter of any triangle is the sum of the lengths of the sides of the triangle triangles are identified not only by their sides but also by their angles since this triangle has one obtuse angle that is one angle which measures more than 90 degrees it can also be called an obtuse triangle a right triangle is a triangle having one right angle an acute triangle is a triangle that has three acute angles that is the measure of each is less than 90 degrees the total number of degrees in the three angles of any triangle is 180 degrees thus whenever we know the size of two angles we can always find the number of degrees in the third one with two triangles we can demonstrate congruency this is another important concept by indicating the line segments this way we can see how triangle ABC fits exactly or coincides with triangle x y z line a b coincides with line x y BC with y z AC with x z angle a coincides with angle X B with y and C with z we see that if two triangles are congruent all six parts of one triangle three angles and three sides are equal respectively to the six parts of the other the triangles are also equal in area congruency will help us demonstrate how we derive this formula for the area of a triangle area equals one-half the base B times the height h first on the base of the triangle we construct a rectangle the rectangle and the triangle both have the same base B and height h we see the triangle AFC is congruent to ADC we know that these two congruent triangles are equal in area in like manner triangle CBE is congruent to cdb we know that these two congruent triangles are equal in area thus triangle AFC and triangle CBE together are equal in area to the area of our original triangle ACB we know that the area of a rectangle equals the base times the height so one half the base times the height must equal the area of a triangle if the original triangle has a base of 10 inches and a height of 5 inches the triangle has an area of 25 square inches one of the most important theorems about triangles was credited to the Greek mathematician Pythagoras it became known as the Pythagorean theorem the Pythagorean theorem applies to all right triangles the hypotenuse is the side opposite the right angle in the theorem the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides in this right triangle the sides are three units four units and five units in length using the Pythagorean theorem let's see if the measure of this area plus the measure of this area is equal to the measure of the third area the square on the hypotenuse we proceed as follows 3 squared is nine four squared is 16. 9 plus 16 equals 25. the square on the hypotenuse using this Theory we can always find the third side if we know the other two remember the problem we saw earlier the Pythagorean theorem will help us find out how much distance this boy is saving we'll use as our unit of measure a section of sidewalk the path which is made by his Crossing is the hypotenuse C and we wish to find its length sides a b and c form a right triangle the length of side a is 20 sections of sidewalk and the length of side B is 15 sections of sidewalk using the Pythagorean theorem we can find the length of the unknown side C since we know the lengths of the other two sides our formula for calculating any one of these distances when the other two are known is a squared plus b squared equals c squared side a measures 20 units 20 squared is 400. side B measures 15 units 15 squared is 225. the sum of these two squares is 625. when we take the square root of 625 we find it is 25. 25 sections of sidewalk is the length of side C the other two sides 20 and 15 total 35. subtracting 25 from 35 gives us 10. the boy has saved himself 10 sections of sidewalk in this problem we have a ladder 24 feet long the distance from the bottom of the ladder to the wall is six feet what then is the distance from the ground to the point where the latter is resting against the wall in this case we want to find the length of side B using the formula a squared plus b squared equals c squared we can make the following calculations side C representing the latter is 24 feet long 24 squared is 576. side a the distance from the bottom of the ladder to the wall is six feet six squared is 36. subtracting 36 from 576 gives us 540. this is the square of side B to find the length of the side we take the square root of 540 which is 23 and 2 10. side B the distance from the ground to the point where the ladder is resting against the wall is 23 and 2 10 feet how to find the length of an unknown side of a right triangle is just one of the important things we have learned about triangles we have also seen that triangles can be identified according to the measures of their sides or their angles we learned to find the area of a triangle by using the formula area equals one-half the base times the height as you continue with your study of mathematics you'll find that the solutions to many kinds of problems depend on your knowledge of triangles [Music] foreign oh yeah everything you wanted to know about triangles but we're afraid to ask uh so behind me um so somebody mentioned like you know when I always gesture to the tell the scanner that uh that hasn't changed it's always the same shoulder but the thing is like so I'm looking at obs's webcam thing it's not a mirror so immediately you fall back to like oh I'm looking in a mirror so I do this and it doesn't it's it's off so yeah so I'm always wrong it seems like so it's like oh I should do nope I should do the opposite of what I think it is uh so anyways behind this we have uh the scanner and let me change this real quick um that was my doorbell uh this title is Martin the Snake Charmer enjoy the large Blue Ocean the island of Sri Lanka the large Blue Ocean Sri Lanka is my homeland and I am Martin the Snake Charmer Sri Lanka lies like a pearl in the Indian Ocean its name is fitting Sri Lanka means The Shining land Sri Lanka is close to India just south east of its southern tip but it is very small in comparison even so our population is always growing today there are over 16 million people Colombo is the capital of my country and it is an important city every day tea and precious stones are shipped out from its kaabas the capital is also the center of world of Tourism which has become an important source of income for both the island and me now it is time to visit my part of the country Gypsy country you can find my family where the roads disappear and the jungle closes in here I am with my friend Raja we're about to go fishing in a nearby lake long time ago my forefathers sailed from India to Sri Lanka which was once an English colony called silon my people have traveled all over the island without ever settling in one place that is why the others call us gypsies or nomads there aren't too many of us on the island we even speak a different language from most our language is and originally comes from Southern India there's another thing that makes us different from the rest of the children in Sri Lanka now John I have never been to school instead we helped support our families by earning money we have a very unusual trade learned from Secrets passed down from father to son for many generations we are snake Charmers The Village I live in houses about 40 families and is located deep in the jungle my family has six people my three sisters my mother my father and me our home is the large Hut the small Hut on the right stores dried foods and other supplies we need these things to protect ourselves against problems in the future like illness or food shortages at night we take down the mats hanging on the wall and roll them out on the floor to sleep on all the boys and men in our village become snake Charmers we begin learning as soon as we can walk my friend Raja and I were only eight years old when we first traveled to the city to earn money for our families we must listen carefully to our fathers when they teach us about snake charming because one bite from a cobra contains enough poison to kill 15 people my grandfather is the chief of the village and when he brings out his snakes everyone gathers to watch foreign in our village works the women are in charge of the heavy work at home they cannot charm snakes but they have learned to read palms so that they too can travel and earn money next year when we are 15 years old most of my friends and I will get married my father has chosen a girl for me and I do not even like her I like another girl who I must meet secretly this is a hard decision for me if I do not marry the girl my father has chosen I may be cast out of my family [Music] my father learned the art of snake charming when he was little and it was his responsibility to pass it on to his son me [Music] the Cobra is a poisonous snake found in the tropical forests of Africa and Asia it is also called the eyeglass snake because of its beautiful design when the Cobra senses danger it lifts up its head and neck and spreads out Its Ribs when it bites it releases a poison into the sword that attacks the nervous system and usually causes the victim to die of suffocation snake Charmers use a flute to attract people and make their act more entertaining [Music] the snake cannot enjoy the music because it has no ears snakes are deaf and react only to vibrations smells and movements snake Charmers can make the Cobra Dance by catching its attention when they move their hands or knees in time to the music here my father shows me how to protect myself from snake bites this magical piece of wood usually keeps the snake from biting it doesn't always work so my father has taught me how to survive a cobra bite first you use a knife to cut away some of the flesh around the bite then you place a small Stone over the sword and press hard according to my father the stone gives out an anti-poison that makes the Snakes poison harmless my family is running out of money so father wants me to go to the city to work I've packed my belongings and I'm ready to walk the long road to Colombo barefoot Raja also needs to earn money so we will journey together I'm glad my friend is coming along because being away from home for a month can get lonely after walking for a few days we come to one of our favorite spots to rest we must set up camp before dark but first it's fun to Splash and play in the water but then we have to check up on our workmates it's important to have a healthy aggressive snake the snakes spend most of their time in our little homemade baskets and they feel as safe and as comfortable as if they were in their own little hole we don't have to worry about feeding them because they usually go several months between meals the Cobra is considered one of the most dangerous snakes in the world it kills about 10 000 people every year even snake Charmers can get killed especially if they're drunk that is why Raja and I have sworn never to drink alcohol some snake Charmers abuse their snakes they sew the mouth shut or beat the snake so much that it cannot bite but we are genuine snake Charmers and we have learned the art so well that we will never have to cheat the first thing we learned is not to show Fear the snake reacts much like a dog if a person is afraid that the snake can get nervous and may bite we think about these things as the sun sets at night our loincloths are what we call sarans become blankets and our shirts and the snakes in the baskets make nice pillows these are the only things we own in the entire world [Music] foreign [Music] [Music] Wireless it is morning now and we must be on our way instead of toothpaste we use sand or colored ashes Elementary my finger is the perfect toothbrush in order to save time we have decided to take a shortcut we must watch out for the wild animals here is a six foot iguana lizard digging for something to eat but it doesn't seem to notice us if we were at home we would have killed it to make a festive dinner but we are in a hurry Colombo is still far away one animal that sometimes attacks is the wild Asian elephant full-grown male can weigh up to six tons we usually find them by water holes where they drink and cool themselves elephants live out as long as we do but they eat a lot more food about 400 pounds of vegetables a day we have decided not to disturb the elephants so we choose another road late in the afternoon we come upon a Buddhist temple we have been raised to worship Buddha like most of people in Sri Lanka we show our Respect by placing flowers and saying a short prayer the Buddhist new year begins in the middle of April and we celebrate with firecrackers now it is raining so we run to the nearest bus stop for shelter we decided to take the bus and save several days of wandering but the buses in Sri Lanka are always full and if we're unlucky we will have to stand all the way to Colombo foreign here we are at the outskirts of our capital city where there are many tourist hotels a good place to begin especially since the money we brought with us is almost gone Raja is trying to get the tourists attention perhaps they would like to see our snakes one time a tourist gave me 300 rupees or ten dollars to see my snake to me this is a great deal of money [Music] soon a crowd of Hotel guests Gathers to them we may be the most exotic site in Sri Lanka foreign so they take the photos to show their friends and relatives who live in Far Away lands that we'll never see us tourists are a means of survival before our show is over Raja goes around and collects money from the audience we just earned 57 rupees a good profit [Music] [Music] now it is time to eat dinner the rice and vegetables packed in newspaper and banana leaves taste good after a hard day of work and travel for about two more weeks we will travel around the city to earn money for our families hopefully we will have thousands of Rupees to carry during the long trip home [Music] this is my life and my story because I am Martin the Snake Charmer [Music] thank you foreign [Music] viruses are a subject we hear about more and more we all know the word virus to most of us it means a cold where the flu but what is a virus is it a plant an animal is it even alive for most of us the only time knowing about viruses becomes important is when we're ill usually a viral infection is just a mild annoyance a few days of discomfort and lots of fluids but an infection of herpes virus can mean outbreaks of painful sores again and again for a lifetime and having this virus flourishing in your blood means a life cut short by AIDS acquired immune deficiency syndrome the first thing that must be learned about viruses is just how incredibly small they are the light microscope we can see protists single-celled plants and animals fractions of a millimeter long highest power of this microscope we can just make out another life form bacteria these dark specks streaming in the currents but even smaller than bacteria and invisible to the light microscope are the viruses to see viruses requires this an electron microscope an average virus is one ten thousandth of a millimeter in diameter turning the magnification up to 50 000 times they come into view dozens and dozens of spherical viruses even at this extreme magnification these viruses look fuzzy and indistinct to get a clear picture of the structure of a virus requires a special technique called x-ray crystallography Dr James Hogle is a researcher in the molecular biology group at Scripps Clinic in California there are two major differences between X-ray crystallography and light microscopy first a lens cannot be used to refocus the X-ray image second it's impossible to measure the X-ray scattered from a single virus particle since a single virus particle is too small to be visualized directly the first step in x-ray crystallography is to bring together trillions of virus particles into a workable Mass this can be done by putting a solution of viruses into a small hard plastic container and covering the container opening with a thin tissue called a membrane the membrane is semi-permeable which means that the small molecules and ions in the virus solution can move out of the chamber but the virus particles cannot the result is that slowly the viruses become less and less soluble and eventually they form crystals each crystal is made of trillions of virus particles packed in symmetric arrays the regularity of the crystal allows the information on the shape of a single virus to be assessed to get this information the virus crystal is placed in a glass tube mounted on an X-ray machine x-rays aimed at the Crystal are scattered into a regular pattern that's recorded on film this is a picture of that scatter it is called an x-ray diffraction pattern many of these patterns become part of a complex mathematical analysis that produces a kind of three-dimensional map the map shows the locations of the atoms in the virus structure with these Maps a knowledge of chemistry and a bit of intuition scientists are able to construct a model of a single virus particle we've learned that typically a virus has two basic parts a protective outer layer of protein sometimes coated with a fatty membrane and an inner core of nucleic acid either DNA or RNA [Music] although most viruses consist of only a few thousand molecules Nature has arranged those molecules into a menagerie of shapes [Music] there are viruses that look roughly spherical under the electron microscope but whose exact geometry is an icosahedron a shape with 20 triangular faces there are also rod-shaped viruses the rod actually has two layers wrapped together [Music] now the center is a strand of nucleic acid while the outside these protein spirally wound in a long helix probably the most dramatically shaped viruses are called phage if you think they look like a spacecraft you're not alone the top of the phage is a hollow protein capsule that contains nucleic acid beneath that is a shaft called a sheath and attached to the sheath are leg like tail fibers a virus carries only the essentials of existence a strand of nucleic acid imprinted with the formula for survival and a strategy to reproduce that precious information generation after generation in the complex world of living creatures who bear minimum Simplicity of the virus is striking compared to a virus even a one-celled animal seems like a great Factory performing and coordinating hundreds of tasks there are cell parts for processing energy parts for locomotion and even parts for maintaining the proper balance of fluids placing a virus into a protist cell would be something like placing a person into the center of a major city both are dwarfed by the large and complex structures that surround them the Machinery of life irises survive how do they reproduce a virus is dependent on a living cell for survival a host cell in a way a virus is a parasite it attacks a host cell and takes over its chemical machinery for making proteins and nucleic acids one of the better understood virus life cycles is phage a virus which attacks bacteria cells the phage begins its assault by attaching itself to the cell wall of the bacteria its attachment is very specific and each type of phage can only attach to a certain type of bacteria next the phage breaks down the cell wall and a nucleic acid from this capsule is injected through the hollow tail into the cell the viral nucleic acid uses the cell's enzymes and organelles to replicate new viral Parts the parts are assembled into new virus particles called virions finally the new phages release an enzyme which weakens the cell wall and the host cell bursts releasing the virions [Music] up to 300 new virus particles can be reproduced in a single host cell this process of viral multiplication is called the lithic cycle [Music] interestingly the lytic cycle does not always happen immediately sometimes rather than producing virions phage nucleic acid incorporates in the host cell DNA each time the cell divides the phage DNA is also reproduced and is spread to more and more cells then suddenly for reasons that are still unclear the phage DNA activates and the destructive lytic cycle begins [Music] once again cell is destroyed and a new generation of phage are released to invade new hosts plant cells also play host to viruses often the vice is injected through the cell wall by insect carriers such as aphids and white flies there's no mistaking the vigorous look of a healthy plant like this melon but when infected with a virus called zucchini yellow mosaic leaves become blistered as the virus destroys broad patches of cells fruit is also susceptible to viral disease here peppermotyl virus causes discoloration and withering of these bell peppers probably the best studied plant virus is this one tobacco mosaic back in the 1890s it was the first virus to be identified as the cause of a disease later it was also used in classic experiments it would reveal the particle nature of a virus animal cells are also invaded by viruses in fact viruses are responsible for a large number of diseases including rabies hepatitis and cholera some viral diseases can even be transmitted between species for example cow pox can be contracted by humans handling diseased herds the list of human viral diseases is also very long yellow fever influenza smallpox herpes and one of the most highly studied human ailments polio the poliovirus attacks certain kinds of nerve cells and for thousands of years it killed and crippled especially children in the spring of 1954 that was about to change Dr Jonas Salk and his research team at the University of Pittsburgh developed a polio vaccine the effort started small Dr sulk and his team immunizing a few thousand students in the Pittsburgh area but soon it became a nationwide mobilization to protect every child against the polio threats Sox vaccine and the vaccine developed later by Albert Saban were a complete success and in countries where the vaccines were used polio all but vanished no more withered legs no more withered lives today vaccines play a part in all of our lives how does a vaccine work it takes advantage of the body's own natural defense against infection cold immunity when a virus or a foreign bacteria enter the body special blood cells called phagocytes seek out and destroy the invader this picture shows phagocytes colored in red in pursuit of several rod-shaped bacteria colored in green as a second line of defense molecules cold antibodies also are produced in response to an infection antibodies are highly specific [Music] the protein shell of a virus triggers the production of a particular type of antibody in turn the antibody is effective only against that particular virus antibodies attach themselves to the protein shell of the virus and render the virus inactive and make it easier for the phagocytes to finish the virus off what a vaccine does is stimulates antibody production and in many cases a vaccine is nothing more than a solution of inactive viruses polioviruses for polio vaccine smallpox viruses for smallpox vaccine the first step in making a vaccine is isolating the virus you want to control this is done by applying viruses to a culture of host cells after a while clear patches in the culture appear showing where cells have been destroyed [Music] which is also the location of the virus antibodies are effective only if there is an exact match at the antigenic site the white spots on the virus shell if these sites change antibodies cannot attach and our immune system cannot protect us some genetic mutations in viruses alter their surface structures such that they're no longer recognized by antibodies this mutation is responsible for periodic epidemics of sunviral diseases such as influenza because a disease virus can have many different varieties will be very changeable it is sometimes impossible to develop a vaccine against it a change virus is hard to stop but there are some things even worse imagine a virus whose Target is the very immune system cells that defend against infection that nightmare has become real is called the AIDS virus human immunodeficiency virus HIV for short they are engulfed by phagocytes but they are not destroyed and they go on to attack the cells that produce antibodies leaving the body defenseless HIV is one of those viruses but does not go into its cell destroying lytic cycle right away at the nucleic acid of HIV can reside in our blood cells for years causing no discomfort no symptoms the only way to see it is with a blood test that fact makes HIV a dangerous epidemic threat medical research to cure or control AIDS is working along several directions from drug therapy to vaccines but the most powerful defense against HIV or any disease virus he's understanding it remember a virus is just a parasite and like any parasite it must be passed from host to host for you know now the AIDS virus is transmitted sexually as well as in Blood and blood products stop the transmission and you stop the virus although viruses have always been a part of our world we have still managed to survive one step at a time we have learned about viral disease and one step at a time we are learning how to stop it thank you [Music] thank you [Music] I'm checking I think the microphone is on I'm sorry about that I was trying to click the scanner sound to work and it turned everything off so my bad um anyways what I had said before was I was reading some of the things on the program notes um about uh uh what does snake charming mean to you if you were a tourist in Colombo if you were Martin or Raja and I should say the snake charming footage was pretty insane awesome but my favorite thing was actually the warthog who is like rubbing his belly on the tree and kind of going oh yeah scratching oh that's good oh yeah I was like man that is that is idyllic um just for some reason resonated with me in in some weird way um so the virus film fascinating um and I should say uh I think we had my family had a recent exposure to covid um because we kind of let our guard down a little bit and so now we have to cancel all of our plans um and I think that that's where we're at in this is um not as many people are getting really sick from covid but um plans are being canceled and so please please be careful uh in this upcoming week there's a lot of family travel and stuff and um even though kova doesn't make a lot of people as sick as it used to um it can make some people really sick and and can really cause some issues so just be cautious and also the flu you know all these things are about getting vaccinated and all that stuff that's my PSA um I'm not interested in anybody who says that vaccines don't work so there you go uh but everybody have a great rest of your weekend um or your weekend coming up and I'll be back on Monday originally I was not going to be here on Monday but all those plans got canceled so um Everybody Take Care and uh I don't feel like I'm gonna get it but I'm taking precautions so everybody we'll see you on Monday bye