Set 05 — Topology & Geometry
Brouwer Fixed-Point Theorem Every continuous self-map of the closed unit ball \(\overline{B}^n\subset\mathbb{R}^n\) possesses at least one fixed point. The result is false for the open ball and also fails in infinite-dimensional Hilbert space without additional compactness assumptions.
One elegant proof proceeds by contradiction: a fixed-point-free map would yield a continuous retraction of the ball onto its boundary, contradicting the non-existence of such a retraction.
Invariance of Domain If \(U\subset\mathbb{R}^n\) is open and \(f:U\to\mathbb{R}^n\) is continuous and injective, then \(f(U)\) is open and \(f\) is a homeomorphism onto its image. Consequently dimension is a topological invariant of Euclidean spaces.
Gauss–Bonnet Theorem For a compact oriented Riemannian surface \(M\) without boundary one has \[ \int_M K\,dA=2\pi\chi(M), \] where \(K\) is the Gaussian curvature and \(\chi(M)\) is the Euler characteristic. The identity links a purely geometric integral to a purely topological invariant.
Hopf–Rinow Theorem On a connected Riemannian manifold the following are equivalent: (i) the manifold is geodesically complete, (ii) the exponential map is defined on the whole tangent space at every point, (iii) every closed bounded set is compact, (iv) the manifold is a complete metric space with respect to the Riemannian distance.
Whitney Embedding Theorem Every smooth \(n\)-dimensional manifold admits a smooth embedding into \(\mathbb{R}^{2n}\). A stronger version asserts that a smooth immersion into \(\mathbb{R}^{2n-1}\) always exists. The optimal ambient dimension is in general sharp.
Angular Version Using AngularJS with angular ui. including angular bootstrap directives and other modules.
Html Version Angulr also provide html version for app does not use angular. using jQuery and html5 to build user freindly app.
Music SPA With angulr layout options, you can build many other apps, we give a music single page application for example.
Google Material Design The Angular Material project is an implementation of Material Design in Angular. js. This project provides a set of reusable, well-tested, and accessible UI.
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In SI units, the coulomb is defined such that the value of the elementary charge is exactly e = 1.602176634×10−19 C.[1][3] Since the 2019 revision of the SI, the seven SI base units are defined in terms of seven fundamental physical constants, of which the elementary charge is one.


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Chart.js

slack

Installation

You can download the latest version of Chart.js from the GitHub releases or use a Chart.js CDN. Detailed installation instructions can be found on the installation page.

Creating a Chart

It's easy to get started with Chart.js. All that's required is the script included in your page along with a single <canvas> node to render the chart.

In this example, we create a bar chart for a single dataset and render that in our page. You can see all the ways to use Chart.js in the usage documentation.

<canvas id="myChart" width="400" height="400"></canvas>
<script>
var ctx = document.getElementById('myChart').getContext('2d');
var myChart = new Chart(ctx, {
    type: 'bar',
    data: {
        labels: ['Red', 'Blue', 'Yellow', 'Green', 'Purple', 'Orange'],
        datasets: [{
            label: '# of Votes',
            data: [12, 19, 3, 5, 2, 3],
            backgroundColor: [
                'rgba(255, 99, 132, 0.2)',
                'rgba(54, 162, 235, 0.2)',
                'rgba(255, 206, 86, 0.2)',
                'rgba(75, 192, 192, 0.2)',
                'rgba(153, 102, 255, 0.2)',
                'rgba(255, 159, 64, 0.2)'
            ],
            borderColor: [
                'rgba(255, 99, 132, 1)',
                'rgba(54, 162, 235, 1)',
                'rgba(255, 206, 86, 1)',
                'rgba(75, 192, 192, 1)',
                'rgba(153, 102, 255, 1)',
                'rgba(255, 159, 64, 1)'
            ],
            borderWidth: 1
        }]
    },
    options: {
        scales: {
            yAxes: [{
                ticks: {
                    beginAtZero: true
                }
            }]
        }
    }
});
</script>