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“Why is there dirt in the snow?” asks Seana as we hike through some freshly fallen snow speckled with dirt and debris. “Maybe it blew off of a roof?” Anthony suggests. “I think it came from the birds and squirrels,” Elijah chimes in. “Or maybe the wind blew it off of the trees?” guesses Quinn. These observations spark a lively conversation about where the dirt came from and how it ended up in the snow. The children wonder if they are eating dirt when they sneak a bite of snow, if the dirt will float to the top when…
Do you think extraterrestrial life exists?If life does exist beyond Earth, what do you imagine? Little green men? Strange and scary creatures? Super intelligent beings?How about marine algae?In “Astronomers Detect a Possible Signature of Life on a Distant Planet,” Carl Zimmer writes about a new study that claims to have discovered the strongest evidence yet of life elsewhere in the universe:The search for life beyond Earth has led scientists to explore many suggestive mysteries, from plumes of methane on Mars to clouds of phosphine gas on Venus. But as far as we can tell, Earth’s inhabitants remain alone in the…
Introduction to AI Math Solvers Mathematics has always been a subject that challenges students, often requiring extra practice and assistance to master. With the rapid advancements in technology, Artificial Intelligence (AI) has stepped in to bridge the gap, offering innovative solutions that help students understand and solve mathematical problems efficiently.AI math solvers are intelligent tools designed to assist learners by providing step-by-step solutions, explanations, and interactive problem-solving experiences. These applications leverage powerful AI algorithms to interpret, analyze, and generate accurate responses to a wide range of math problems. From simple arithmetic to complex calculus, AI math solvers are transforming the…
A basic type of problem that occurs throughout mathematics is the lifting problem: given some space that “sits above” some other “base” space due to a projection map , and some map from a third space into the base space , find a “lift” of to , that is to say a map such that . In many applications we would like to have preserve many of the properties of (e.g., continuity, differentiability, linearity, etc.). Of course, if the projection map is not surjective, one would not expect the lifting problem to be solvable in general, as the map to…
A brief month ends. Time to round up the happenings… A number system with no zero. This month I added a snazzy new line to my CV: “math puzzle columnist for Science News.” My stuff will appear on the back page of the magazine (alternating months with science-themed crosswords). In the future, expect ghosts, mud, village fools, and Michael Phelps’s towel. But for the inaugural puzzle, I decided to go with a numerical oddity. I first came across it in Reckonings: Numerals, Cognition, and History, by anthropologist Stephen Chrisomalis, and it has tickled me ever since. The zero-free number system.…
Things are invented. Things are discovered. And somehow there’s an arc of progress that’s formed. But are there what amount to “laws of innovation” that govern that arc of progress? There are some exponential and other laws that purport to at least measure overall quantitative aspects of progress (number of transistors on a chip; number of papers published in a year; etc.). But what about all the disparate innovations that make up the arc of progress? Do we have a systematic way to study those? We can look at the plans for different kinds of bicycles or rockets or microprocessors.…
In this chapter we will prove that in a triangle, a median divides it into two triangle of equal area. Given:Given below is the triangle ABC in which AD is the median.Also AN is the altitude of the triangle To Prove:Median AD divide the triangle into two equal parts.i.e. Area (ABD) = Area (ADC) Proof:Consider triangle ABD.Area (ABD) = 1/2 x BD x AN –> eq (1)Now consider triangle ADC.Area (ADC) = 1/2 x DC x AN – -> eq (2) Since AD is the median of triangle, we can write;BD = DCSo eq (2) can be written aslArea (ADC)…
Emergency Fund for Young Professionals – Behavioral Economics Barriers to Emergency Fund CreationPsychological and Behavioral BarriersEmergency fund for young professionals? Let’s go! Behavioral economics studies identify several psychological and behavioral barriers that impede young professionals from building emergency funds. Key barriers include present bias (the tendency to prioritize immediate consumption over future savings), low financial confidence, and limited financial knowledge. Present bias leads individuals to undervalue the importance of future financial security, resulting in insufficient emergency savings. Overconfidence or underconfidence in financial decision-making can also deter proactive saving behaviors, as individuals may either overestimate their ability to handle emergencies or…
There are 4 basic operations. The graphic organizer below shows what these operations are along with some other important terms. Read the lesson or take the quiz to see how much you know. Teachers! Use this graphic organizer to easily help your students understand this important math concept. Basic Operations Key Terms Explained Addition Terms Addends: the numbers being added.Sum: the answer to the addition problem. Subtraction Terms Minuend: the number you are subtracting from.Subtrahend: the number that is to be subtracted from the minuend.Difference: the answer to the subtraction problem. Multiplication Terms Factors: the numbers being multiplied.Product: the answer…
We know that the number written as sum of the place-values of its digits is called the expanded form of a number. Standard Form Expanded Form 20,37,81,405 = 20,00,00,000 + 0 + 30,00,000 + 7,00,000 + 80,000 + 1,000 + 400 + 0 + 5 In expanded form of a number, the number is shown according to the place values of its digits. This is shown here:In 2385, the place values of the digits are given below: Hence, 2385 = 2000 + 300 + 80 + 5Thus, 2000 + 300 + 80 + 5 is the expanded form of 2385.Again, …