Euler's formula, e^{pi i} = -1, is one of the most famous expressions in math, but why on earth is this true? A few perspectives from the field of group theory can make this formula a bit more intuitive.

Euler's formula, e^{pi i} = -1, is one of the most famous expressions in math, but why on earth is this true? A few perspectives from the field of group theory can make this formula a bit more intuitive.

Worried about black holes? Consider this: Every time you accelerate - you generate an event horizon behind you. The more you accelerate away from it the closer it gets. Don't worry, it can never catch up to you, but the Unruh radiation...

Today we’re going to talk about how computers understand speech and speak themselves. As computers play an increasing role in our daily lives there has been an growing demand for voice user interfaces, but speech is also terribly...

MIT researcher Deb Roy wanted to understand how his infant son learned language -- so he wired up his house with videocameras to catch every moment (with exceptions) of his son's life, then parsed 90,000 hours of home video to watch...

This video is chapter 2 in my series on special relativity, and it covers spacetime diagrams, rotational and translational symmetry of both time and space, how certain transformations preserve distances (measured in terms of a...

In this, THE FIRST EPISODE of Crash Course Physics, your host Dr. Shini Somara introduces us to the ideas of motion in a straight line. She talks about displacement, acceleration, time, velocity, and the definition of acceleration. Also,...

The US economy has been expanding wildly for two centuries. Are we witnessing the end of growth? Economist Robert Gordon lays out 4 reasons US growth may be slowing, detailing factors like epidemic debt and growing inequality, which...

How do babies learn so much from so little so quickly? In a fun, experiment-filled talk, cognitive scientist Laura Schulz shows how our young ones make decisions with a surprisingly strong sense of logic, well before they can talk.

In this, THE FIRST EPISODE of Crash Course Physics, your host Dr. Shini Somara introduces us to the ideas of motion in a straight line. She talks about displacement, acceleration, time, velocity, and the definition of acceleration. Also,...

Continuing with last week's introduction of calculus, Shini leads us through the ways that integrals can help us figure out things like distance when we have several other key bits of information. Say, for instance, you wanted to know...

Why is the electric potential energy of unlike charges negative? Why does it decrease as they get closer? In this Flipping Physics lesson, we graph electric potential energy vs. distance for a two-point charge system and use the shape of...

Summary:

How to visualize Minkowski four dimensional spacetime and relativity using light cones and world lines. These are three spatial dimensions and one time dimension in the universe. With these 4...

Pupil outcome: I can use my understanding of various graphical representations to solve problems. Key learning points: - Data can be presented in various formats. - A fuller picture can be obtained when considering more data. - Multiple...

Pupil outcome: I can construct scatter graphs from data presented in a number of different ways using technology. Key learning points: - Scatter graphs can be constructed quickly using spreadsheets. - Scatter graphs can be constructed...

Pupil outcome: I can compose one and ten million in different ways. Key learning points: - Unitising can be used to support the composition of 7- or 8- digit numbers. - If 250 is one quarter of one thousand, then 250,000 is one quarter...

Pupil outcome: I can read and interpret points from a graph to solve problems. Key learning points: - If you have one value, you can use a linear graph to find its pair. - The pair of values will satisfy the linear equation. - If the x...

Pupil outcome: I can construct a table from a histogram. Key learning points: - A frequency table can be used to construct a histogram - A histogram can be used to construct a frequency table - Data is sometimes collected using uneven...

Pupil outcome: I can deduce that the area under a speed-time graph gives the distance travelled and deduce how this may be calculated. Key learning points: - Distance travelled is calculated by multiplying speed and time. - This is...

Pupil outcome: I can appreciate that a function is a mathematical relationship that uniquely maps a set of numbers onto another set of numbers. Key learning points: - A function has a set of inputs and outputs. - For any valid input,...

Pupil outcome: I can construct bar charts from data. Key learning points: - Data presented as a list can be represented as a bar chart - Data presented in a table can be represented as a bar chart - The type of data determines how the...

Pupil outcome: I can estimate from scatter graphs. Key learning points: - When a linear trend can be identified, you can draw a line of best fit. - The line of best fit should represent the trend of the data. - The line of best fit can...

Pupil outcome: I can interpret time series graphs, including commenting on trends. Key learning points: - The graph can be used to estimate a frequency at a given time - Time series graphs can help us spot underlying trends or systematic...

Pupil outcome: I can construct time series graphs. Key learning points: - Time series graphs are a visual representation - Time series graphs plot frequency over time - Consecutive points are joined by straight line segments